- #1
soopo
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Homework Statement
How can you integrate the following?
[tex] \int \sqrt {R^2 - x^2} dx [/tex]
The Attempt at a Solution
Integration by parts does not seem to be a solution here.
Integration by substitution works to some extend:
Let [itex] x = R sin(u) [/itex].
We get
[tex] \int \sqrt {R^2 - x^2} dx = \int Rcos(u) (R^2 + 2R^2 sin^2(u)) Rsin(u) du[/tex]
[tex] = \int R^4 cos^2(u) sin(u) (1 + 2sin^2(u) ) du [/tex]
I cannot see how to integrate this easily.
Perhaps, there is a better way to do this.