## anonymous one year ago Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^3,y=16x about the x-axis.

1. SolomonZelman

your boundaries are $$y=x^3$$ and $$y=16x$$ and it is rotated about the x,axis correct?

2. SolomonZelman

x-axis *

3. anonymous

yes

4. SolomonZelman

that will look like a washer method|dw:1437943945723:dw|

5. SolomonZelman

do you know the washer method?

6. SolomonZelman

(don't be ahsamed not to know, if you don't know it is ok. the only person i can not help is the silent one)

7. anonymous

i do but have trouble with the set up

8. SolomonZelman

ok, lets figure the limits of integration together I will name them differently for our convinience $$f(x)=16x$$ $$g(x)=x^3$$

9. SolomonZelman

lets find the points where these two functions intersect

10. SolomonZelman

16x=x³ 16=x² (and disregard negative x solutions because we are only in the 1st quadrant)

11. SolomonZelman

x=?

12. anonymous

4

13. SolomonZelman

yes, and one more?

14. anonymous

0

15. SolomonZelman

yes

16. SolomonZelman

So our limits of integration (for the region bounded by 16x and x³) is (x=0 and x=4) \ (i.e. the intersection points after which the region stops)

17. SolomonZelman

So far we know $$\large\color{slate}{\displaystyle\int\limits_{0}^{4}}$$

18. anonymous

okay got it and hw to determine inner vs outer for the formula

19. SolomonZelman

yes, and if you were to graph the two functions $$f(x)=16x$$ and $$g(x)=x^3$$ then for all values on the interval [0,4] (which is the interval we need) it is true that f(x)≥g(x)

20. SolomonZelman

So, g(x) is always below the f(x) in our case. right?

21. SolomonZelman

(you can test it using any value between 0 and 4)

22. anonymous

okay great thanks , makes more sense now , you were a big help!!

23. SolomonZelman

you are thinking me already, we aren;t done yet, aren we?

24. SolomonZelman

thanking*

25. anonymous

i just struggle with the set up I just worked out that practice problem and solved it form there

26. SolomonZelman

ok, but, just to make sure can you show me your integral that you will set up?