حمّل تطبيق منهاجي الجديد

منهاجي صار أسرع من خلال التطبيق
  أتحقق من فهمي

أتحقق من فهمي

التكامل غير المحدود

الاقتران الأصلي

أتحقق من فهمي صفحة (9):

أجد اقتراناً أصلياً لكلّ من الاقترانين الآتيين:

(a) f(x) = 5x4

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f left parenthesis x right parenthesis equals 5 x to the power of 4 end cell row blank cell G left parenthesis x right parenthesis equals x to the power of 5 plus C end cell end table end style

(b) f(x) = -9x-10

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

التكامل غير المحدود

أتحقق من فهمي صفحة (11):

أجد كلاً من التكاملات الآتية:

(a) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

(b) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

(c) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

(d) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

خصائص التكامل غير المحدود

أتحقق من فهمي صفحة (12):

أجد كلاً من التكاملين الآتيين:

(a) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

(b) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

 

أتحقق من فهمي صفحة (13):

أجد كلاً من التكاملات الآتية:

(a) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

(b) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

(c) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root plus K end cell row blank cell C left parenthesis 0 right parenthesis equals 2 square root of 0 squared plus 16 end root plus K end cell row blank cell 0 equals 8 plus K end cell row blank cell K equals negative 8 end cell row blank cell C left parenthesis t right parenthesis equals 2 square root of t squared plus 16 end root minus 8 end cell row blank cell C left parenthesis 3 right parenthesis equals 2 square root of left parenthesis 3 right parenthesis squared plus 16 end root minus 8 equals 2 end cell end table end style

إعداد : شبكة منهاجي التعليمية

09 / 02 / 2023

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