Find the volume of the solid generated by revolving the plane region bounded by the equations about the indicated line(s).
Y = x, y = 0, x = 4

(a). the x-axis
(b). the Y-axis
(c). the line x=4
(d). the line x=6

Question

Find the volume of the solid generated by revolving the plane region bounded by the equations about the indicated line(s).
Y = x, y = 0, x = 4

(a). the x-axis
(b). the Y-axis
(c). the line x=4
(d). the line x=6

anonymous · Answer

I have sketched out the equation. I have done a and b, but I am not sure if I got them right and I am not sure how to attempt the other problems. 

(a). $$\pi \int\limits_{0}^{4} (x)^2 dx = 64\pi/3$$
(b). $$\pi \int\limits_{0}^{4}(4)^2-(y)^2dy = 128\pi/3$$

Can someone help me with the other 2?

domebotnos · Answer

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anonymous · Answer

Not sure

anonymous · Answer

Can you help me with this?

domebotnos · Answer

sorry i havent gotten to this yet...

anonymous · Answer

Its okay, do you know of anyone else that could? I have a huge test tomorrow and my teacher gave me a review guide and I am not sure how to do this type of problem.

perl · Answer

part a) is correct

anonymous · Answer

@perl can you help me with the rest?

perl · Answer

sure

perl · Answer

|dw:1426572293309:dw|

perl · Answer

|dw:1426572322293:dw|

perl · Answer

since y = x ,  x = y, so you have 4 - y

perl · Answer

$$

\Large \pi \int_{0}^{4}(4-y)^2~dy

$$

perl · Answer

|dw:1426572509320:dw|
\Large \pi \int_{0}^{4}(4-y)^2~dy