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I have to evaluate
$$\int^1_{-1} \int^{ \sqrt {1-x^2}}_{ - \sqrt {1-x^2}} \int^1_{-\sqrt{x^2+y^2}}dzdydx$$
using spherical coordinates.
This is what I have come up with
$$\int^1_{0} \int^{ 2\pi}_0 \int^{3\pi/4}_{0}r^2\sin\theta d\phi d\theta dr$$
by a combination of sketching and substituting spherical coordinates.
After evaluating I obtain this integral to equal 3.57.
where as the first one evaluates to 5.236.
These are so difficult :(
$$\int^1_{-1} \int^{ \sqrt {1-x^2}}_{ - \sqrt {1-x^2}} \int^1_{-\sqrt{x^2+y^2}}dzdydx$$
using spherical coordinates.
This is what I have come up with
$$\int^1_{0} \int^{ 2\pi}_0 \int^{3\pi/4}_{0}r^2\sin\theta d\phi d\theta dr$$
by a combination of sketching and substituting spherical coordinates.
After evaluating I obtain this integral to equal 3.57.
where as the first one evaluates to 5.236.
These are so difficult :(