Question

hey guys i have a math final tomorrow and i do not know how to solve like this problem : evaluate the definite integral : integral ( 1 to 2 ) 24(x^2-6)^5x dx = .. please could someone tell me how to start solving these problems i have tried many times but i keep getting wrong answer :(

Answer 1

Is the question\[\int_1^224(x^2-6)^5xdx\]

Answer 2

yes , but how can i solve it

Answer 3

Let u = x^2 -6
du = ... ?

Answer 4

so du = 2x ?

Answer 5

then 1/2x du = dx ?

Answer 6

1/2x du = dx <- yes

Answer 7

Next step is to change the limit.
Remember we let u = x^2 -6
When x = 1, u = 1^2-6 = -5
When x = 2, u = ...?

Answer 8

-2

Answer 9

\[\int_1^224(x^2-6)^5xdx\]\[=\frac{1}{2}\int_1^224(x^2-6)^5(2xdx)\]Note: 2xdx = du. Now, we do the u-sub:
\[=\frac{1}{2}\int_{-5}^{-2}24(u)^5(du)\]So far so good?

Answer 10

yess

Answer 11

Now, do the integration :P

Answer 12

thats it ?

Answer 13

omg thank you so much ^^

Answer 14

You're welcome! Remember to do the integration LOL.

Answer 15

Yup I will .. :P