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:

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[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)