# evaluating integral

#### dorkymichelle

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
delete this

double post?

#### dorkymichelle

oops, must've clicked submit two times, how do i delete this? or do i need a moderator?

#### matheagle

MHF Hall of Honor
hit edit and look for where it says delete