## yuki 5 years ago the base of the solid has a region defined by y=x^2 and y=e^x the plane section perpendicular to the y-axis has a shape of sqrt(x). find the volume of the solid

1. anonymous

3d ?

2. anonymous

i cannot solve for the intervals

3. Yuki

come on guys I know you want to show off your skills :) Yes, MathMind, it's in 3D

4. anonymous

oh its 3d ok

5. Yuki

we are allowed to use a calculator to find the intersections and integrate

6. Yuki

this problem is not solve by hand

7. anonymous

do you know what the intervals are ?

8. anonymous

i think i know how to solve it one second

9. Yuki

oops, I guess e^x does not intersect x^2 twice so why don't we use x=2 as our other boundary.$e^x = x^2$ x = -.703

10. Yuki

so the picture I just provide never happens

11. anonymous

now it looks solvable

12. anonymous

$\int\limits_{-.703}^{2}(e^x-x^2)dx=[e^x-x^3/3]||(-.703, 2)$

13. anonymous

$\int\limits_{-.703}^{2}\sqrt{(e^x-x^2)}dx=$

14. anonymous

3.192926228

15. Yuki

YEEEEEEESSSSSSSSS!!!!!