Hi,

I want to determine the volume covered by a spherical function with three constants (a, b, c) given as-

f = a* Cos[Theta]^3 + b* Cos[Theta] Sin[Theta]^2 - c* (Cos[Phi] - 3 Cos[3 Phi]) Sin[Theta]^3

So I tried the Integration -

Integrate[Sin[Theta]*f, {Theta, 0, Pi}, {Phi, 0, 2 Pi}]

Which gives the o/p to be zero, suggesting that the function is symmetric on positive and negative axes irrespective of the values of the three constants. Since I am only interested in determining the volume enclosed by the function, I also tried integrating the absolute value of it, but due to the presence of three constants, it did not succeed.
Would appreciate any suggestion to Integrate this function. thanks