Asked by Top
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 5x^2, y = 5x, x ≥ 0; about the x-axis
V = ???
Sketch the region
y = 5x^2, y = 5x, x ≥ 0; about the x-axis
V = ???
Sketch the region
Answers
Answered by
Steve
Given the region shown at
http://www.wolframalpha.com/input/?i=plot+y%3D5x^2%2Cy%3D5x
and recalling that the volume of a washer with thickness dx is
pi (R^2-r^2) dx
where R=5x and r = 5x^2
it should be clear.
You can verify your answer using shells, where the volume of each shell is
2pi r h dy
where r = y and h = √(y/5) - y/5
http://www.wolframalpha.com/input/?i=plot+y%3D5x^2%2Cy%3D5x
and recalling that the volume of a washer with thickness dx is
pi (R^2-r^2) dx
where R=5x and r = 5x^2
it should be clear.
You can verify your answer using shells, where the volume of each shell is
2pi r h dy
where r = y and h = √(y/5) - y/5
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