Thread: A few Calc II Final Exam Questions (Setup ONLY)

Just a few setup problems... If I knew what strategy to use to evaluate these integrals, I'd be better off. That's all I need to know for the following:

1.) Find the volume of the solid formed by revolving the region bounded by the graphs of and y = 0 about the x-axis.

2.) Evaluate:



3.) Evaluate:

Originally Posted by Aryth

Just a few setup problems... If I knew what strategy to use to evaluate these integrals, I'd be better off. That's all I need to know for the following:

1.) Find the volume of the solid formed by revolving the region bounded by the graphs of and y = 0 about the x-axis.

2.) Evaluate:



3.) Evaluate:

For the first problem, use the disc method and integrate:

Thanks, that helped tremendously.

2.



The integral represents the area under the upper half of a circle of radius 4. So:

3.

Making the subs:

which is a standard one

I'm not sure about #2, but for #3 the antiderivative of is .

Originally Posted by o_O

2.



The integral represents the area under the upper half of a circle of radius 4. So:

Wow, thanks. That was completely different then what I was expecting. But the answer was correct.

Originally Posted by Aryth

Wow, thanks. That was completely different then what I was expecting. But the answer was correct.

Yeah, I tried using trig substitution on that one. Not the way to go about it, apparently.

Well you could do a trig sub:



So you get:



etc. etc.

But as you can see having that little insight with recognizing the form of a circle speeds up the process.