Question

How do you use the Fundamental Theorem of Calculus to find the derivative of `f(x)=int_1^(x)sqrt(e^t+sin(t))dt` ?

Answer 1

Fundamental Theorem of Calculus

`d/{dx}int_a^x f(t) dt=f(x)`

This theorem illustrates that differentiation can undo what has been done to `f` by integration.

Let us now look at the posted question.

`f'(x)=d/{dx}\int_1^xsqrt{e^t+sint}dt=sqrt{e^x+sinx}`

I hope that this was helpful.