The region between the graph f(x)=x^(1/2) and the x-axis for x∈[0,16] is revolved about the line y=8. Which integral will determine the volume of the solid that is generated?

I got π(x-64)dx, x∈[0,16] using the yA=1/2[(f(x))^2 - (g(x))^2]dx x∈[a,b] equation, but the answer is ∫π[64−(8−x^(1/2))^2]dx x∈[0,16]. No idea where I went wrong, but maybe this isn't the right equation to use?

Question

The region between the graph f(x)=x^(1/2) and the x-axis for x∈[0,16] is revolved about the line y=8. Which integral will determine the volume of the solid that is generated?

I got π(x-64)dx, x∈[0,16] using the yA=1/2[(f(x))^2 - (g(x))^2]dx x∈[a,b] equation, but the answer is ∫π[64−(8−x^(1/2))^2]dx x∈[0,16]. No idea where I went wrong, but maybe this isn't the right equation to use?

amistre64 · Answer

are we using shells or discs?

amistre64 · Answer

shells add the area of rectangles:  2pi r

discs add the area of circles:  pi r^2

amistre64 · Answer

it looks like disc method to me

amistre64 · Answer

|dw:1442770213833:dw|