- #1

jsun2015

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## Homework Statement

1. R is the shaded region in the 1st quadrant bounded by the graph of y=4ln(3-x), the horizontal line y=6, and the vertical line x=2

Find the volume of the solid when revolved about the horizontal line y=8

2. Let R be the region in the 1st quadrant enclosed by the graphs of f(x)=8x^3 and g(x) =sin(∏x) from x=0 to 1

Write, but do not evaluate, an integral expression for the volume of the solid generated when R is rotated about the horizontal line y=1

## Homework Equations

V=∏[itex]\int[/itex](outer radius[itex]^{2}[/itex]- inner radius[itex]^{2}[/itex]) dx from a to b

## The Attempt at a Solution

1. outer radius = 8-4ln(3-x), inner radius = 8-4ln(3-x)

2. I thought of multiple possibilities

outer radius =1-sin(∏x) or 1-8x^3, inner radius =1-(8x^3) or 1-sin(∏x)

1. Why isn't the inner radius 8-4ln(3-x)?

2. Why Cant the outer radius be 1-sin(pix)?

Why Cant the outer radius be 1?

Why Cant the inner radius be 1-8x^3?

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