## A community for students. Sign up today

Here's the question you clicked on:

## anonymous 4 years ago Evaluate the intragural. 3y(7+2y^2)^1/2 dy

• This Question is Closed
1. anonymous

Does anyone have any idea?

2. TuringTest

$u=7+2y^2$$du=4ydy$$\int3y(7+2y^2)^{1/2}dy=\frac34\int u^{1/2}du$

3. anonymous

Wait. So how did that 3y in front of the u just dissapear?

4. TuringTest

I just pulled it outside the integral sign

5. TuringTest

$\int cf(x)dx=c\int f(x)dx$

6. anonymous

Even though its 3y(u)^1/2? I thought if it was 3+ you could

7. anonymous

Im just not getting where the y went

8. TuringTest

$u=7+2y^2$$du=4ydy\to ydy=\frac14du$$\int3y(7+2y^2)^{1/2}dy=3\int (7+2y^2)^{1/2}ydy$I just pulled the three out and put ydy together, so now I can sub in my expressions for 7+2y^2 and ydy that I got above:$3\int (7+2y^2)^{1/2}ydy=\frac34\int u^{1/2}du$let me know if something is still eluding you.

9. TuringTest

a little slower on the last step:$3\int (7+2y^2)^{1/2}ydy=3\int(u)^{1/2}(\frac14du)=\frac34\int u^{1/2}du$

10. anonymous

I sorta get it I think. Just not sure how ydy becames (1/4du) when du did equal 4ydy. Shouldnt it be (1/4du)y?

11. TuringTest

the u sub works such that we need to wind up with $\int u^ndu$watch the terms that we get from our substitution$u=7+2y^2$$du=4ydy$$ydy=\frac14du$so we rearrange our integral so that we replace ydy by 1/4du if we had ydu we couldn't integrate, so that would not help

12. TuringTest

$3\int (7+2y^2)^{1/2}(ydy)=3\int(u)^{1/2}(\frac14du)=\frac34\int u^{1/2}du$see how ydy got replaced?

13. anonymous

Oh I think I get it. Thanks a lot

14. TuringTest

u-subs can be tricky at first, but with practice it's a flash :D

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy