Thread: Integration

I was given a problem about revolving a region around the x-axis and finding the volume of the region. I know for sure that this is the correct integral for the particular problem: (notation: exp(x)=e^x)

pi(exp(3x)^2)-pi(exp(x))^2

And the upper bound is 2 and the lower bound is 0.

I split the integral into two separate integrals and I was able to solve the second part (pi(exp(x))^2) but I was told by another math tutor that the first integral couldn't be solved by rules of integration, but instead by estimation. She said simpson's rule would be best, but I thought we needed an "n" to solve for that...and even then I'm not quite sure I understand what she meant. Help!
Thanks a lot!

Originally Posted by amaya

I was given a problem about revolving a region around the x-axis and finding the volume of the region. I know for sure that this is the correct integral for the particular problem: (notation: exp(x)=e^x)

pi(exp(3x)^2)-pi(exp(x))^2

And the upper bound is 2 and the lower bound is 0.

I split the integral into two separate integrals and I was able to solve the second part (pi(exp(x))^2) but I was told by another math tutor that the first integral couldn't be solved by rules of integration, but instead by estimation. She said simpson's rule would be best, but I thought we needed an "n" to solve for that...and even then I'm not quite sure I understand what she meant. Help!
Thanks a lot!

can't be integrated using elementry functions we could use simpsons rule to approximate it. Remember with approximation rules like simpson we choose n.

We can integrate it by using its power series.



so evaluating at we get



integrating we get...

I was able to solve the (exp(x))^2 because it turns out being Exp(2x) which I can solve. The one I'm having problems with is:

integral from 0 to 2 of: 9(x^2) (nine "x" squared)

help!

Someone isn't paying attention. I think it's "another math tutor".

is a bit of a problem.