Page 1 of 1

0568 #24

Posted: Thu Oct 16, 2008 3:10 pm
by gaucho85
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.

Posted: Thu Oct 16, 2008 3:52 pm
by moo5003
Edit: I think I got it

e^(x+t) = e^x * e^t

e^x Int[ e^t ] = e^x * [e^x^2 - 1]

= e^(x+x^2) - e^x

Now take the dertivative

e^(x+x^2) * (1+2x) - e^x

Plug in 1

3e^2 - e

Posted: Thu Oct 16, 2008 4:17 pm
by Nameless
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