Question

Find F (x) from the given F'(x)
F'(x) = $7x^2$ - 2x + 3, whose graph passes through the point M(1, 5).

Answer 1

$F^{\prime }\left(x\right)=7x^2-2x+3$

$\int F^{\prime }\left(x\right)dx=7.\frac{x^3}{3}-x^2+3x+c=F\left(x\right)$

Given F(1)=5

$F\left(1\right)=7.\frac{1^3}{3}-1^2+3\left(1\right)+c=5\Rightarrow c=\frac{13}{3}$

$F\left(x\right)=7\frac{x^3}{3}-x^2+3x+\frac{13}{3}$