Question

(Definite integral)

x * e^(x^2) dx from 1 to 3

Answer 1

u sub.

Answer 2

Oh, yeah I had a question about it:

Answer 3

u have
\[\large \int xe^{x^2}\,dx \]
try the substitution \(u=x^2\)

Answer 4

go ahead

Answer 5

Sorry for the confusion, I've worked it out already, but I was just wondering why it's 1/2 and not 1/4 (see my attached image):

Answer 6

what u did is wrong!! @TJ91x

Answer 7

Uh oh. :(

Answer 8

you would have to leave the 1/2u inside the integrand and it would cancel with u = e^(x^2)
\[\int\limits_1^3 xe^{x^2}\, dx = \frac{1}{2} \int\limits_{e}^{e^9} du\]

Answer 9

ooops... i goofed.

Answer 10

yeah, let u = x^2

Answer 11

you don't have an extra e^(x^2) for du.

Answer 12

Ohh, okay, I see. I'm trying the substitution with x^2 instead of e^x^2

Answer 13

Oh boy, that worked out much better:

Answer 14

there you go

Answer 15

Thanks guys. :)

Answer 16

you're welcome!

Answer 17

if \(u=x^2\) then \(du=2x\,dx\) or \(du/2=x\,dx\) so
\[\large \int_1^3xe^{x^2}\,dx=\int_1^3e^u\,\frac{du}{2}=
\frac{1}{2}\int_1^3e^u\,du=\frac{1}{2}e^u\Biggr|_1^3=
\frac{1}{2}e^{x^2}\Biggr|_1^3 \]
\[\large =\frac{1}{2}(e^9-e) \]