Question

Find F ′(x) for F(x)= ∫ from a= x^2 b=3 for the equation sin(t^2)dx

A. –2xsin(x^4)

B. sin(x^4)

C. –sin(x^4)

D. sin(3^2) – sin(x4)

Answer 1

$F(x)=\displaystyle\int_{x^2}^3\sin(t^2)\,\mathrm dt=-\int_3^{x^2}\sin(t^2)\,\mathrm dt$

By the fundamental theorem of calculus, differentiating gives

$F'(x)=-\sin((x^2)^2)(2x)=-2x\sin(x^4)$

so the answer is A.