Question

Evaluate the definite integral.[3,-3] 4xe^(x^2+1)dx

Answer 1

you can do a substitution here,
x^2+1 = u
then du =... ?

Answer 2

2x

Answer 3

how about
du = 2x dx ?

Answer 4

Yes I can get that far, but I am trying to find the ending answer I know will be some fraction multiplied by ((e^9^2+1)-(e^-9^2+1))

Answer 5

ok....
so first you need to change limits also.
when x= 3, u=... ?
when x = -3, u=... ?

Answer 6

9 and -9

Answer 7

sorry 9 and 9

Answer 8

ahh sorry 10 and 10

Answer 9

hmm...just a sec

Answer 10

if you were to graph this function, you'll notice it's symmetrical about the origin

basically you can rotate it 180 degrees and it will line up with itself

Answer 11

what this means is that integrating this from x = -k to x = k, for any positive number k, will yield 0

Answer 12

and because you got integral endpoints of 10 and 10 means you're integrating this new function of u from x = 10 to x = 10...which is a line with no area at all

Answer 13

yeah, in other words, since you have same upper and lower limits, you can use the property that
\(\int \limits_a^af(x)dx=0\)

Answer 14

k got it!

Answer 15

How about [3,0] 15xe^(x^2)

Answer 16

here, you can substitute x^2 = u

Answer 17

Du= 2x dx

Answer 18

yes,
so, x dx = du/2
x^2=u
substitute these in your integral
and don't forget to change the limits

Answer 19

So my new limits are 3 and 0

Answer 20

Sorry 9 and 0

Answer 21

yes.

Answer 22

So now I say 1/2 (e^9)?

Answer 23

or (e^9-1)

Answer 24

let me check..
(15/2) e^u du
---> (15/2) e^u
---> (15/2) [e^9 - e^0]
---->(15/2)[e^9-1]

Answer 25

howd you get 15/2

Answer 26

your Question has 15 in it
"How about [3,0] 15xe^(x^2)"

Answer 27

yes But I could not determine where the factor in the 15x

Answer 28

'where the factor in the 15x' <---- what ? i didn't get you.

Answer 29

\(\large \int \limits_0^315xe^{x^2}dx=15\int \limits_0^3e^{x^2}(xdx)=15\int \limits_0^9e^u(du/2)\)
right ?

Answer 30

and then,
(15/2) e^u du
---> (15/2) e^u
---> (15/2) [e^9 - e^0]
---->(15/2)[e^9-1]

Answer 31

I meant whereTO factor in the 15x.. I see now

Answer 32

ok, good :)
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