I'm struggling to find the limits need for this equation to give me the answer the question requires. $z=\sqrt{x^2+y^2}$ and $x>=0$ for the integral $\int\int\int(xe^{-z}) dV$.
I've got that z is between 0 and infinity and theta between 0 and $\pi$ and R between 0 and z but when that is integrated i can't get 4, which is what the question requires the answer to be.
Can anyone tell me where i've gone wrong?
try limits of r bounded by z and 0. limits of z bounded by zero and infinity. And your limit for theta should be between pi/2 and -pi/2. The limit for theta is because the cone is between the posotive y-axis and the negative y-axis. so theta is pi/2 at the posotive y-axis and theta is negative pi/2 when it goes anti-clockwise from the posotive x-axis.