Evaluating Triple Integral: $\int\int\int_H(x^2+y^2) dV$

[squenshl]

How would I evaluate the triple integral $$\int\int\int_H(x^2+y^2)$$ dV,
where H is the region bounded x² + y² = 1, y = x, y = 0, z = 0, z = 2

 

[slider142]

It is sector of a cylinder. Try cylindrical coordinates. A very simple integral results.

 

[whitay]

I was about to say Moment of Inertia about the z axis. But no!.

Um yes when you convert to cylindrical co-ordinates remember the $$cos^{2}(x) + sin^{2}(x) = 1$$ and you should be left with $$r^{2}$$. Making the integration easier. Don't for get the Jacobian.

 

[squenshl]

Cheers. Thought so