## anonymous 5 years ago find the volume of the solid obtained by rotating the region lying between the curves around the y-axis. y=sinx y=e^x x=pi/2 x=pi

1. watchmath

$$\int_{\pi/2}^{\pi }2\pi x(e^x-\sin x)\,dx$$

2. anonymous

can you help me with the steps?

3. amistre64

the graph doesnt makes sense ......

4. amistre64

you appear to have a boundary between boundaries

5. amistre64

or, that means that you spin it around the y axis; the part that is between ..got it

6. amistre64

7. amistre64

if so; shelling is fine; 2pi {S} (xe^x - xsin(x)) dx ; [pi/2, pi]

8. amistre64

but it might be uglier than the disc method to integrate

9. amistre64

e^x =y x = ln(y); is ln^2(y) easy to integrate? havent tried it meself lol

10. amistre64

http://www.wolframalpha.com/input/?i=int%28pi%28ln%28y%29%29^2%29dy+from+0+to+1 says its 2pi for that bit :)

11. amistre64

thnx :)

12. anonymous

i have couple more review questions can you help me amistre64?

13. amistre64

i can...maybe