What is the volume obtained by rotating a region bounded by a given curve?

[Jbreezy]

Homework Statement

Find the volume obtained by rotating the regon boudned by the given curve about the specified axis

Homework Equations

The Attempt at a Solution

y = secx, y = cosx, 0 <= x < = pi/3

This is what I set up.

V = ∏∫ (secx +1 )^2 - (cosx +1)^2 dx

I said R was secx - (-1) and r is cosx -(-1)

 

[Mark44]

Homework Statement

Find the volume obtained by rotating the regon boudned by the given curve about the specified axis

Homework Equations

The Attempt at a Solution

y = secx, y = cosx, 0 <= x < = pi/3

This is what I set up.

V = ∏∫ (secx +1 )^2 - (cosx +1)^2 dx

I said R was secx - (-1) and r is cosx -(-1)

Looks OK, assuming you are rotating the region about the line y = -1, which is info you didn't provide. When you post a problem, remember to include the complete problem statement.

 

[Jbreezy]

Yeah I'm doing it about x = -1. Thanks dude. Sorry.

 

[arildno]

Why the 1's?
The radii in the cross-sectional disks are specified with the function values.
Thus, your integrand is sec^2(x)-cos^2(x)

I assumed it was about y=0

 

[Jbreezy]

Yeah well that is because I made a mistake in my post and left out that is was about y = -1.

 

[Mark44]

Yeah I'm doing it about x = -1. Thanks dude. Sorry.

Yeah well that is because I made a mistake in my post and left out that is was about y = -1.

Apparently you aren't clear, either.

 

[Jbreezy]

Ha. Lack of sleep