## anonymous 4 years ago Find the volume generated by revolving about the x-axis the area bounded by xy = 9, the x-axis and lines x = 3 and x=9

1. amistre64

|dw:1324412465826:dw|

2. amistre64

something similar to this right?

3. anonymous

Yess

4. amistre64

then we can integrate, or sum up the areas of circles, generated by the function from 3 to 9 i believe

5. anonymous

May I please see a full work out please?

6. anonymous

@ amistre64 Alright

7. amistre64

$\sum_{3}^{4}\pi[f(x)]^2\ \Delta x$ $\pi \int_{3}^{9}(\frac{9}{x})^2dx$

8. amistre64

|dw:1324412686951:dw|

9. amistre64

if we take any arbitrary circle created by spinning this about the x axis; we get an area of: pi (y)^2 pi (9/x)^2 the volume generated is then adding up all the circles made from x=3 to x=9

10. TuringTest

are you still stuck? can you not integrate$\pi\int_{3}^{9}\frac{9^2}{x^2}dx$? or are you having another problem?

11. anonymous

@ amistre64 Alright

12. anonymous

is it 18pi?

13. amistre64

http://www.wolframalpha.com/input/?i=integrate+pi*%289%2Fx%29%5E2+from+3+to+9 18pi looks good to me