Check my work: Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 5.

v = ∫[0,2] 2πrh dx

r=5-x and h=x-x^2/2

v = ∫[0,2] 2π (5-x) (x-x^2/2) dx = 16π/3

v = ∫[0,2] π (R^2-r^2) dy

R=5-y and r=5-√ (2y)

v = ∫[0,2] π ((5-y) ^2 - (5-√ (2y)) ^2) dy = 16π/3

Question

Mathematics

Ralphie

3 August, 08:59

Check my work: Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 5.

v = ∫[0,2] 2πrh dx

r=5-x and h=x-x^2/2

v = ∫[0,2] 2π (5-x) (x-x^2/2) dx = 16π/3

v = ∫[0,2] π (R^2-r^2) dy

R=5-y and r=5-√ (2y)

v = ∫[0,2] π ((5-y) ^2 - (5-√ (2y)) ^2) dy = 16π/3

+1

Answers (1)

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Odie · Answer 1

You are correct! Good job! I started this using the washer method and found that it was much more tedious than using the shell method, which worked very well and very easily. Very good work!