Question

Find F (x) from the given F'(x)
F'(x) = sin 2x + $3x^2$ and F(0) = 2.

Answer 1

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

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

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

Given F(0)=2

$F\left(0\right)=-\frac{1}{2}+0^3+c=2$

$c=\frac{5}{2}$

$F\left(x\right)=-\frac{\cos x}{2}+x^3+\frac{5}{2}$