Evaluate the following integral by converting to polar coordinate system: ∫∫(√4-x^2-y^2)dA, where R={(x,y)| x^2+y^2 ≤ 4, x ≥ 0|}

Answer 1

change to polar. rdrdO = dxdy. r**2=x**2+y**2

int(int(sqrt(4-r**2)rdrdO))

substitution: u=4-r*82

int(int(sqrt(u)dudO))

16Pi/3