Volume of solid from rotating y=x between x=2 and x=4 about x=1

[jzsc]

Homework Statement

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

y=x, y=0, x=2, x=4; about x=1

The Attempt at a Solution

one of the radii is x=y but I am not sure how to find the other one and the interval? Please explain this one to me. Thanks!

 

[SammyS]

Homework Statement

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

y=x, y=0, x=2, x=4; about x=1

The Attempt at a Solution

one of the radii is x=y but I'm not sure how to find the other one and the interval? Please explain this one to me. Thanks!

Hello jzsc. Welcome to PF !

Which are you using, the disk method or the washer method ? Until you decide that, you can't specify a radius.

 

[jzsc]

thank you SammyS! I am using the washer's method

 

[e^(i Pi)+1=0]

$2\Pi\int x f(x) dx$

The x is serving as the distance from the y-axis (the radius), so if you're rotating around x=1 rather than x=0...

(I don't know how to put the a & b above and below the integrand)

 

[ehild]

$2\Pi\int x f(x) dx$

(I don't know how to put the a & b above and below the integrand)

$2\Pi\int_a^b x f(x) dx$

ehild