Yet another question from 0568 -

h(x) = integral from 0 to x^2 of e^(x+t) dt

h'(1) = ?

Can someone point out where I went wrong, please?

h'(x) = e^(x+x^2)*(2x) - e^(x+0)

h'(1) = 2e^2 - e

but the correct answer is 3e^2 - e.

thanks.

## 0568 #24

Yet another question from 0568 -

h(x) = integral from 0 to x^2 of e^(x+t) dt

h'(1) = ?

Can someone point out where I went wrong, please?

h'(x) = e^(x+x^2)*(2x) - e^(x+0)

h'(1) = 2e^2 - e

but the correct answer is 3e^2 - e.

thanks.

this is just special case of Leibniz Integral rule

http://mathworld.wolfram.com/LeibnizIntegralRule.html