Question

Find the volume of the solid by rotating the graph 9x^2+4y^2=36 about the y-axis

Answer 1

always a good start to draw a picture with these
to do that you need to recognize what kind of graph this is, and where the intercepts are

Answer 2

Yup. I did, and my intercepts were x=2 y=3

Answer 3

because we're going around y, I think we should integrate along y and use disk method
so we need an expression for the area of each disk, which means we need the radius

Answer 4

the radius of each disk is\[r=f(y)=\frac23\sqrt{9-y^2}\]so the area of each disk is\[A(y)=\pi r^2=\frac{\pi}3(9-y^2)\]