Volume of area between 2 curves: y=x^2, y=x+2, rotated about x-axis

[clockysockz]

24 a Find the area of the region bounded by the functions [imath]y=x^2[/imath], [imath]y=(x-2)^2[/imath], and the [imath]x[/imath]-axis.
24 b The area bounded by the curve [imath]y=x^2[/imath] and the line [imath]y=x+2[/imath] is rotated about the [imath]x[/imath]-axis. Find the exact volume of the solid formed.

I need help for question 24 b. The answer for 24a for 2/3 units ^2.

 

[Dr.Peterson]

View attachment 35042I need help for question 24 b. The answer for 24a for 2/3 units ^2.

Please show what you have tried, so we can see where you need help:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...

www.freemathhelp.com

 

[MarkFL]

Suppose that for 24a, we observe we can write:

\(\displaystyle A=2\int_0^1 x^2\,dx=\frac{2}{3}\)

Does this symmetry give you a hint how to easily find 24b?

 

[BigBeachBanana]

24a)


24b)