Integrate the function over the domain using polar coordinates:
f(x,y) = xy
x >= 0, y >=0, x^2 + y^2 <= 4
I did:
\(\displaystyle x = rCos(\theta)\)
\(\displaystyle y = rSin(\theta)\)
\(\displaystyle f( rCos(\theta), rSin(\theta) ) = rCos(\theta) rSin(\theta) = r^2Cos(\theta)Sin(\theta)\)
\(\displaystyle \LARGE \int_0^\frac{\pi}{2} \int_0^2 r^2Cos(\theta)Sin(\theta) drd\theta = \frac{4}{3}\)
Book says the answer is 2? Where have I made a fool of myself?
f(x,y) = xy
x >= 0, y >=0, x^2 + y^2 <= 4
I did:
\(\displaystyle x = rCos(\theta)\)
\(\displaystyle y = rSin(\theta)\)
\(\displaystyle f( rCos(\theta), rSin(\theta) ) = rCos(\theta) rSin(\theta) = r^2Cos(\theta)Sin(\theta)\)
\(\displaystyle \LARGE \int_0^\frac{\pi}{2} \int_0^2 r^2Cos(\theta)Sin(\theta) drd\theta = \frac{4}{3}\)
Book says the answer is 2? Where have I made a fool of myself?