Question

Let \(R\) be the region bounded by the curves \(y^2 = 2x\) and \(x = 3y\). What is the volume of the solid generated by rotating \(R\) about the \(y\)-axis?

Name: Let R be the region bounded by the curves y^2 = 2x and x = 3y. What is the volume of the solid generated by rotating R about the y-axis?
Uploaded: 2023-01-30T11:32:10-08:00
Duration: 1 min 30 s
Channel: Madhur L
Description: Let R be the region bounded by the curves y^2 = 2x and x = 3y. What is the volume of the solid generated by rotating R about the y-axis?

          Let \(R\) be the region bounded by the curves \(y^2 = 2x\) and \(x = 3y\). What is the volume of the solid generated by rotating \(R\) about the \(y\)-axis?

Added by Juan M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

01/30/2023

Step 1

To find the points of intersection, we can substitute x = 3y into the first equation: y^2 = 2(3y) y^2 = 6y y^2 - 6y = 0 y(y - 6) = 0 y = 0 or y = 6 So the points of intersection are (0,0) and (6,18). Show more…

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Let R be the region bounded by the curves y^(2)=2x and x=3y. What is the volume of the solid generated by rotating R about the y-axis? Let R be the region bounded by the curves y2 = 2c and c=3y.What is the volume of the solid generated by rotating R about the y-axis?