By using Washer method, we can find the volume of the solid.
Since the curve is bounded by x=1 and x=2, then y-values are bounded between 0 and 1. If you graph this curve and bounds, you'll see that we have to split the integral into 2 separate integrals.
First Integral
The first one will be bounded between y=0 and y = 1/2.
...
By using Washer method, we can find the volume of the solid.
Since the curve is bounded by x=1 and x=2, then y-values are bounded between 0 and 1. If you graph this curve and bounds, you'll see that we have to split the integral into 2 separate integrals.
First Integral
The first one will be bounded between y=0 and y = 1/2.
From y=0 to y=1/2, the area being revolved around x=-1 is just a rectangle. The outer radius is x=2 and inner radius is x=1.
So,
Second Integral
Now, the second region is bounded from y=1/2 to y=1 and the outer function is x=1/y and the inner function is x=1.
So,
Adding it all together
Now that we have the volumes of the 2 different regions, we can add them together to get the total volume.
So,
is the final answer
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