Question

Hey, I'm having some trouble with sketching solids with double integrals.

Answer 1

\[\int\limits \int\limits_R \sqrt{9-y^2} dA\] R = [0,4] x [0, 2]

Answer 2

I'm not really sure how to sketch this solid

Answer 3

letting z = 9-y^2

Answer 4

\[z = \sqrt{9-y^2}\]

Answer 5

notice that the defining function of the solid is independent of "x" and dependent on "y". and infact, a parabolic dependence on "y"

Answer 6

let us re-write it as \[\int_{x=0}^4\int_{y=0}^2\sqrt{9-y^2}\,(dx\,dy)\]

Answer 7

Right

Answer 8

dydx no? :P

Answer 9

moreover, the variables "x" and "y" are independent

Answer 10

and "z" goes from \(-\infty\) to \(\infty\)