kentm
- 16
- 1
I was just starting to get comfortable with integrals in the easy situations, and then with substitution in some of the more difficult cases. I thought it might be kind of fun to try and calculate pi with the area under the semi circle:
\begin{math}y=\sqrt{9-x^2}\end{math}
I figured the proper integral for this would be:
\begin{math}4\int_0^3 \sqrt{9-x^2}\end{math}
but then I realized I'm not fully equipped to take that anti derivative. Substitution never fully gets rid of the x, and I'm unaware of a standard anti derivative that could be used to calculate such an integral. How would you go about this?
\begin{math}y=\sqrt{9-x^2}\end{math}
I figured the proper integral for this would be:
\begin{math}4\int_0^3 \sqrt{9-x^2}\end{math}
but then I realized I'm not fully equipped to take that anti derivative. Substitution never fully gets rid of the x, and I'm unaware of a standard anti derivative that could be used to calculate such an integral. How would you go about this?