Integrals Problem

Question

Let y=∫₁^cos(x) (−9t+10sin(t))dt. Use the Fundamental Theorem of Calculus to find y′.

y′=

Answer 1

y' = (- 9cos(x) + 10sin(cos(x)))(- sinx)

Answer 2

By Fundamental Theorem of Calculus

y'=d/dx(∫-9t+10sin(t)dt) where ∫ is from 1 to cos(x)

First you calculate:

∫-9t+10sin(t)dt (where ∫ is from 1 to cos(x)) which will give you a function with variable x

Then you calculate the derivative with respect to x