# HELP! y=-x+e^(x^2)*integral from 0 to x of e^(-t^2)dt find y'?

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• Jun 25th 2010, 05:16 PM
jdk022
HELP! y=-x+e^(x^2)*integral from 0 to x of e^(-t^2)dt find y'?
Can anyone help me solve this problem?
• Jun 25th 2010, 05:24 PM
Also sprach Zarathustra
Quote:

Originally Posted by jdk022
Can anyone help me solve this problem?

$y=-x+e^{x^2}\int_0^x e^{-t^2}dt$

$y'=-1 + 2xe^{x^2}\int_0^x e^{-t^2}dt+e^{x^2}\cdot e^{-x^2}=$

$=-1 + 2xe^{x^2}\int_0^x e^{-t^2}dt+1=$

$2xe^{x^2}\int_0^x e^{-t^2}dt$

or:

$y'=2x(y+x)=2xy+2x^2$

For more information read here:

Fundamental theorem of calculus - Wikipedia, the free encyclopedia