Find the surface area of revolution by revolving the curve y

Find the surface area of revolution by revolving the curve y=1/2x^2 about the y-axis from x=0 to x=2. show all work

Formula is 2x ds

ds= (1+y\'^2)

y\'= x

So we have int x (1+x^2)^(1/2) dx from x=0 to x=2

Antiderivative is 1/3 (1+x^2)^(3/2)

Evaluating at limits we have

1/3 (5^(3/2)- 1)

$Find the surface area of revolution by revolving the curve y=1/2x^2 about the y-axis from x=0 to x=2. show all workSolutionFormula is 2x ds ds= (1+y\'^2) y\'= x$

Find the surface area of revolution by revolving the curve y

Solution

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