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Parametric equations to find surface area

  • #1
784
11

Homework Statement


Which of the following integrals represents the area of the surface obtained by rotating the parametric curve
x=t-t^2
y=(4/3)t^(3/2)
1<t<2

Homework Equations


A = integral ( 2pi(y) * sqrt( 1+ (dy/dx)^2))dx


The Attempt at a Solution


I solved for dy/dx and got
12(t^1/2) / (9-18t)
and then plug (1-2t)dt in for dx
and (4/3)t^3/2 for y

If i plug these all in and algebra correctly will i get the correct answer?
How do i include the information that it's being rotated around the x-axis into my equation?
 

Answers and Replies

  • #2
34,053
9,912
If i plug these all in and algebra correctly will i get the correct answer?
That should give the right answer. You can simplify your dy/dx, by the way.

How do i include the information that it's being rotated around the x-axis into my equation?
Your equation at (2.) takes care about that.
 

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