Question

Asked Nov 6, 2019

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find the exact area of the surface obtained by rotating x=t^3,y=t^2, 0<t<1 about the x-axis.

Step 1

y=t^2 so t= sqrt(y)

x=t^3= (sqrt(y))^3 = y^(3/2)

x=y^(3/2) (graphed this equation)

Step 2

Use the surface area formula .

There plug x=t^3 and y=t^2 then simplify.

Step 3

When t=0 , then u=4

When t=1 then u=1...

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