evaluating integral

• May 13th 2010, 11:02 PM
dorkymichelle
evaluating integral
Evaluate the integral by interpreting it in terms of areas.
37. $\displaystyle \int^0_{-3} (1+\sqrt{9-x^2})*dx$
the answer is $\displaystyle 3+\frac{9}{4}*\pi$
Where .. the heck did $\displaystyle \pi$ come from?
I was trying to do
$\displaystyle \frac{b-a}{n}$
$\displaystyle = \frac{0-3}{n}$
$\displaystyle =\frac{-3}{n}$

and then $\displaystyle x_{i}$ as $\displaystyle \frac{-3i}{n}-3$
then plugging $\displaystyle x_{i}$ into $\displaystyle f(x)*dx$ then solving for the limit. It came out to be a super complicated root problem so I look in the back to see if I'm in the right track.. and theres a $\displaystyle \pi$ in the answer...
I think I'm missing something here... how is this integral end up having a $\displaystyle \pi$?
• May 13th 2010, 11:05 PM
matheagle
delete this
double post?
• May 13th 2010, 11:15 PM
dorkymichelle
oops, must've clicked submit two times, how do i delete this? or do i need a moderator?
• May 13th 2010, 11:20 PM
matheagle
hit edit and look for where it says delete