Think about what the washer method involves -- why it's called the "washer" method.Blonde1551 said:Homework Statement
Find volume of the solid generated by revolving the region bounded by x = y^2, x=4
about the line x = 5
Homework Equations
the washer method from c to d ∏∫ R(y)2 - r(y)2
The Attempt at a Solution
I set r(y) = 1 and R(y)= y^2
and got the integral from 0 to 2 of ∏∫(y^2)^2-(1)^2
I got an answer of 16.96 but i know this is wrong because the back of the book gives a different answer. Please tell me where I went wrong.
The formula for finding the volume of a solid revolving region bounded by x=y^2, x=4 about x=5 is V = π∫(4-y^2)^2 dy, where the limits of integration are from y=0 to y=2.
The variable y represents the distance from the axis of revolution (x=5) to the curve x=y^2.
The limits of integration are determined by finding the intersection points between the two equations x=y^2 and x=4. These intersection points are y=0 and y=2, which become the lower and upper limits of integration, respectively.
No, this formula is specifically for a solid revolving region bounded by x=y^2, x=4 about x=5. Different shapes and boundaries will require different formulas for finding the volume.
Changing the axis of revolution can greatly affect the volume of the solid. In this problem, changing the axis from x=5 to any other value would result in a different volume. In general, the volume of a solid revolving region is proportional to the distance from the axis of revolution.