Change of variables in multiple integrals
Multivariable and vector calculus · Mathematics
Study notes
Q: Evaluate the integral over the unit disk of (x^2 + y^2) dA using polar coordinates. x^2 + y^2 = r^2, dA = r dr dtheta. Limits: r 0 to 1, theta 0 to 2pi. Integral = integral 0 to 2pi of integral 0 to 1 of r^2 times r dr dtheta = integral 0 to 2pi of [r^4/4] 0 to 1 dtheta. = integral 0 to 2pi of (1/4) dtheta = (1/4)(2pi) = pi/2.