Double or triple integral that equals 30

[Mandanesss]

For my assignment I have to come up with a really complex double or triple integral that equals 30.
Would you mind giving me some ideas?

 

[HallsofIvy]

How about picking some region in the plane (a circle perhaps) that has area 30 or a region in 3d (a sphere perhaps) that has volume 30 and set up the corresponding integral?

 

[Gib Z]

Set up the integrals as a function and solve accordingly, I will start an example for a single integral.

Choose a function, set that as the integrand, set one limit of the integral as another variable, and solve the new function to 30.

eg I choose an integrand x^2.

So I let $$f(t)=\int^t_0 x^2 dx$$

Apply the fundamental theorem of calculus we get
$$f(t) = \frac{t^3}{3}$$
So now we can let f(t)=30 and solve accordingly.

Do the same but for a double or triple integral.

 

[nicksauce]

1) Pick a function
2) Pick a region/volume
3) Integrate
4) Normalize to 30