Fundamental Theorem of Calculus Part 1

[Guderian93]

I don't fully understand how to use FTC1 to find a derivative when the upper bound of the integral isn't x. Can you please explain in detail how to solve this problem:

Find the derivative: f(x) = integral of sin^4(t) dt with a lower bound of 2 and an upper bound of 1/x

Is the answer -sin^4(x) / x^2 ? Is it -sin^4(1/x) / x^2 ?

 

[stapel]

I don't fully understand how to use FTC1 to find a derivative when the upper bound of the integral isn't x.

The process involves the Chain Rule. Take a look at the second example in the box on this page.