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

Question

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

anonymous · Answer

3d ?

anonymous · Answer

i cannot solve for the intervals

yuki · Answer

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

anonymous · Answer

oh its 3d ok

yuki · Answer

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

yuki · Answer

this problem is not solve by hand

anonymous · Answer

do you know what the intervals are ?

anonymous · Answer

i think i know how to solve it one second

yuki · Answer

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

yuki · Answer

so the picture I just provide never happens

anonymous · Answer

now it looks solvable

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

3.192926228

yuki · Answer

YEEEEEEESSSSSSSSS!!!!!