to polar coordinates. If your calculator or CAS evaluates definite integrals
numerically, use it to find the integral correct to three decimal places.
If not, use Simpson's Rule:
Solution: The domain of the integral is a quarter-circle:
Converting to polar coordinates,
Using Maple to find the integral to three decimal places is 0.587:
f:=(r,t)->r*exp(-(r^4)):
int(int(f(r,t),t=0..Pi/2),r=0..1):
evalf(");
by:sh