Volumes: y = x^3, y = 0, x = 2, about the x-axis

[xc630]

Hi I would like osme help with this problem

I have to find the volume of the solid generated by revolving the region by the lines and curves about the x-axis

I am given y= x^3, y=0, x=2

I did the integral from 0 to 1 of [(x-x^2)^2 - 0^2] dx

then x^2-2x^3-x^4 dx

then 1/3x^3 - 8x^4- a/5x^5 for the anitderivative pluggin in 1 and 0 I got 1/2-8-1/5 which is negative and doesnt make sense. Please help!

 

[galactus]

Try shells:

\(\displaystyle \L\\2{\pi}\int_{0}^{8}(y^{\frac{4}{3}})dy\)

Try washers:

\(\displaystyle \L\\{\pi}\int_{0}^{2}(64-x^{6})dx\)

 

[xc630]

can u explain the concepts of shells and washers. have never been intorduced to those methods

 

[galactus]

How do you study solids of revolution and not know washers and shells?.

That's what you use. That's how it's done.

I am sorry, I can not teach that here. Try to find a good calc book and/or math instructor.

 

[xc630]

okayyy