evaluating integral

Dec 2009
103
0
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 \(\displaystyle \pi\)?
 

matheagle

MHF Hall of Honor
Feb 2009
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delete this

double post?
 
Dec 2009
103
0
oops, must've clicked submit two times, how do i delete this? or do i need a moderator?
 

matheagle

MHF Hall of Honor
Feb 2009
2,763
1,146
hit edit and look for where it says delete