What is the Leibniz Rule for Integrals?

[MathewsMD]

For the function F(x) = _x^x2∫(3t² - 4/(1-t))dt find dF(x)/dx

Attempt:

= d/dx [t³ - 4lnl 1-t l)]l^x2_x
= d/dx [x⁶ + 4lnl 1-x² l - x³ - 4lnl 1-x l
= 6x⁵ - 8x/l1-x²l - 3x² + 4/l1-xl

This is what I got. I was hoping to hear feedback on whether or not it's correct. I'm also wondering if there's any other method to solve this problem. Thanks!

 

[SteamKing]

What you have doesn't appear to be quite right.

This article explains the Leibniz Rule for various types of integrals.

http://en.wikipedia.org/wiki/Leibniz_integral_rule

Scroll down to the section "Variable limits form" and use the formula there.

 

[MathewsMD]

What you have doesn't appear to be quite right.

This article explains the Leibniz Rule for various types of integrals.

http://en.wikipedia.org/wiki/Leibniz_integral_rule

Scroll down to the section "Variable limits form" and use the formula there.

Thanks!