please explain how you would do it without graphing the equations...thanks The i

Question

please explain how you would do it without graphing the equations...thanks

The integral represents the volume of a solid of revolution. 2 pi integral^8_0 (y + 5) squareroot 8 - y dy (a) Identify the plane region that is revolved. plane region bounded by x = y + 5, x = 0, y = 0 plane region bounded by y = squareroot 8 - x, x = 0, y = 0 plane region bounded by x = squareroot 8 - y, x = squareroot y + 5, y = 0 plane region bounded by x = squareroot 8 - y, x = y + 5, y = 0 plane region bounded by x = y + 5, x = 0, y = 6 plane region bounded by x = squareroot 8 - y, x = 0, y = 0 (b) Identify the axis of revolution. revolved about the y-axis revolved around line x = -5 revolved about the x-axis revolved around line y = 5 revolved around line y = -5 revolved around line y = 8

Explanation / Answer

Clear shell method here....

2pi * r * h

And the r = sqrt(8-y)
and h = y + 5

So, since h = y +5,
it means revolution is about the line y = -5

And the h = sqrt(8 - y)
So, x = sqrt(8 - y)

Now, you will notice that we have
x = sqrt(8 - y) , x = 0 and y = 0
revolved about the line y = -5

So, a)
option F

And b)
option E

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