verify my setup

[hank]

Ok another one of those volumes for a region revolving around the x-axis type problems.

The region is bounded by y = sqrt(25 - x^2) and y = 3.

Here's my setup:

V = pi S[0 to 4] [sqrt(25-x^2)]^2 - [3]^2 dx

Does this look right?

I got the limits by setting sqrt(25-x^2) = 3 and solving for x. (equals 4).

Then R(x) - sqrt(25-x^2) and r(x) = 3.

 

[galactus]

Looks good. Getting better.

Washers:

\(\displaystyle \L\\{\pi}\int_{0}^{4}((25-x^{2})-3^{2})dx\)

Shells:

\(\displaystyle \L\\2{\pi}\int_{3}^{5}y(\sqrt{25-y^{2}})dy\)

 

[hank]

That's what I thought.

I come up with the answer 192pi/3.

does that look right?

 

[galactus]

No , should be \(\displaystyle \frac{128{\pi}}{3}\)

 

[hank]

Ha!

Awesome, book says it should be 256pi/3.

LOL.

I hate this book.

 

[galactus]

The book is correct. We forgot to take the limits from -4 to 4.

\(\displaystyle \L\\{\pi}\int_{-4}^{4}(16-x^{2})dx\)


Here's what it looks like: