Leibniz Formula/Fundamental Theorem of Calculus

[drmatth]

Homework Statement

The problem is attached as a picture.

Homework Equations

I believe the theories relevant to the equation are the Leibniz formula and the first or second fundamental theorem of calculus, I have two books and one lists the first theorem as the second and vice-versa. The theorem containing the derivative of the integral is the one I am looking at. The chain rule is also involved as well.

The Attempt at a Solution

I am stuck, my teacher explained how to do it today in class. I tried to integrate the function by reducing the power of sin(t^2) to (1/2)(1-cos2t) then differentiating that. I have no idea if that gives me correct answer as my teacher explained it an entirely different way using chain rule and fundamental theorem of calculus. When I check my answer and the answer I get from WolframAlpha by plugging in 1 after everything. They are very close but they are not the same, both answers were done in exact form, so no rounding issues.

Thanks

 

[Poopsilon]

Your trig identity you used is for $sin^2(x)$ not $sin(x^2)$, this site should help with your problem http://mathworld.wolfram.com/LeibnizIntegralRule.html

 

[drmatth]

Ah you are correct, thank you for pointing that out. I came across that site and others like it but the notation was a bit confusing for me. As I was typing this response I came across the explanation he was giving me today.

http://www2.bc.cc.ca.us/resperic/Math6A/Lectures/ch5/3/FundamentalTheorem.htm

Towards the bottom of the page under the Leibniz Integral Rule. I think if I study this a bit I may be able to come up with the correct answer.

Thank you for your help!