Double or triple integral that equals 30

1. Oct 11, 2007

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?

2. Oct 11, 2007

HallsofIvy

Staff Emeritus
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?

3. Oct 11, 2007

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.

4. Oct 11, 2007

nicksauce

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