Question

Evaluate the integral.

Answer 1

\[\int\limits_{-3}^{3}xe ^{-x ^{2}+2}\]

Answer 2

*include dx after the equation

Answer 3

u-substitution:
Let u = -x^2 + 2, du = ...?

Answer 4

@Callisto du= -2x

Answer 5

Isn't it supposed to be including dx?
du=-2x dx

Answer 6

dv=x?

Answer 7

u = -x^2 + 2, du = -2x dx
Now, we need to change the limit as well.
When x=3, u = -(3)^2 + 2 = 7
When x = -3, u=...?

Answer 8

-7

Answer 9

then do i add them up or something like that?

Answer 10

Sorry, When x=3, u = -(3)^2 + 2 = -7

Answer 11

\[\int\limits_{-3}^{3}xe ^{-x ^{2}+2}dx\]\[=-\frac{1}{2}\int\limits_{-3}^{3}e ^{-x ^{2}+2}(-2xdx)\]Do the u-substitution here\[=-\frac{1}{2}\int\limits_{-7}^{-7}e ^{u}(du)\] So far so good?

Answer 12

yeah

Answer 13

Then, we are done.

Answer 14

but where did you get the -1/2 from?

Answer 15

In what form would the final answer be in though?

Answer 16

\[\int\limits_{-3}^{3}xe ^{-x ^{2}+2}dx\]\[=(-\frac{1}{2})(-2)\int\limits_{-3}^{3}xe ^{-x ^{2}+2}dx\]\[=(-\frac{1}{2})\int\limits_{-3}^{3}e ^{-x ^{2}+2}(-2xdx)\]

Answer 17

Integer

Answer 18

@Callisto -1/2e^-x^2+2 isnt coming out right

Answer 19

What do you mean?

Answer 20

as the final answer

Answer 21

The final answer is an integer.

Answer 22

for all my other "evaluate the integer" problems i just got stuff without \[\int\limits_{-3}^{3}\]

Answer 23

Yes, you don't need to integrate it, after doing the u-sub. Or even without u-sub.

Answer 24

so just to be clear can you tell me what the final answer would be?
im not trying to sound like an idiot or anything I just have one more attempt...

Answer 25

Maybe you can work it out?

Answer 26

1) Something you need to know:
\(\int_a^a f(x)dx =0\)