إجابات أتحقق من فهمي

التكامل غير المحدود

a) f(x) = x¹⁰ + C

b) f(x) = x^-11 + C

a) $\int$ 9dx = 9x + C

b) $\int$ x^-4dx = - $\frac{1}{3}$ x^-3 + C

c) $\int$$\sqrt[6]{x}$dx = $\frac{6}{7}$ $\sqrt[6]{x^2}$ + C

a) $\int$(2x⁴ + 3x³ – 7x²)dx = $\frac{2}{5}$ x⁵ + $\frac{3}{4}$ x⁴ - $\frac{7}{3}$ x³ + C

b) $\int$(5x^{${}^{\frac{3}{2}}$} + 3x²)dx =  2x^{${}^{\frac{5}{2}}$} +  x³ + C

a) $\int$$\frac{2x^2 + 4}{x^2}$ dx =  2x - 4x^-1 + C

b) $\int$ $\frac{x+2}{\sqrt{x}}$dx = $\frac{2}{3}$ x^{${}^{\frac{2}{3}}$} + 3x ^{${}^{\frac{1}{2}}$}+ C

c) $\int$ (2x + 3) (x – 1)dx = $\frac{2}{3}$x³ + $\frac{1}{2}$x² – 3x  + C

a) $\int$(x – 4)⁶dx = $\frac{1}{7}$ (x – 4)⁷ + C

b) $\int$ $\sqrt{x + 1}$ dx = $\frac{2}{\sqrt[3]{{(x + 1)}^3}}$ + C

f(x) = 2x² – 2x + 3

a) v(t) = 2t² – 4t + 5 m/s

b) s(t) =  $\frac{2}{3}$ t³ – 2t² + 5t m

c) v(1) = 3 m/s       a(1) = 0 m/s²