Question

Find the volume of the solid generated by revolving the region between the parabola = 2 + 1 and the line = 3 about the line = 3.

Answer 1

Answer:

Line x=3 cuts the parabola at points (3,2–√),(3,−2–√) . We can divide the solid into thin discs of width dy. Each such disc will have volume πr2dy . Now radius of any disc will be the distance of the parabola from the line in x direction. So, subtract the x coordinates to get r=3−(y2+1)=2−y2 . So, the volume of the discs are π(2−y2)2dy . Integrate it from −2–√ to 2–√ to get total volume.

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