Volumes help needed please (1 Viewer)

[blackops23]

Hi, I did a question but ended up getting a ridiculous answer, please anyone correct my solution and outline what i did wrong, because I can't seem to see where i went wrong.

Thanks guys.

Q. Find the volume of solid of revolution formed when the area between y=4x^2 and y=x^3 is rotated about the x-axis.

My solution:

Intersection occurs at x=0 and x=4

V= (pi)*[0integrand4 :16x^4 - x^6]
=pi*[(16x^5)/5 - (x^7)/7] -- limits 0 and 4

basically my final answer was 2941.24

So what did I do wrong?
Help greatly appreciated thank you.

 

[funnytomato]

Hi, I did a question but ended up getting a ridiculous answer, please anyone correct my solution and outline what i did wrong, because I can't seem to see where i went wrong.

Thanks guys.

Q. Find the volume of solid of revolution formed when the area between y=4x^2 and y=x^3 is rotated about the x-axis.

My solution:

Intersection occurs at x=0 and x=4

V= (pi)*[0integrand4 :16x^4 - x^6]
=pi*[(16x^5)/5 - (x^7)/7] -- limits 0 and 4

basically my final answer was 2941.24

So what did I do wrong?
Help greatly appreciated thank you.

The only thing that may be "wrong" is that you didn't have a unit. Apart from that, I got exactly the same answer.

I think it's a rather large number because the radii(y values) of the cylinders are quite large.

 

[SpiralFlex]

Finding the intersection points,





,

Volume of the solid generated about the x axis =







with limits of 0 and 4.