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Use of integration to find area

  • Thread starter Calpalned
  • Start date
  • #1
297
6

Homework Statement


Find the area enclosed by the curve x = t^2 -2t, y = t^0.5 and the y axis

Homework Equations


Area of a parametric curve = ∫g(t) f'(t) dt, where g(t) = y and f(t) = x

The Attempt at a Solution


I believe that the limits of integration by be found by setting x and y equal to each other and solving for y. Do I still use the given equation, or do I have to modify it as this question asks about the y-axis, not the x-axis.

Thanks
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618

Homework Statement


Find the area enclosed by the curve x = t^2 -2t, y = t^0.5 and the y axis

Homework Equations


Area of a parametric curve = ∫g(t) f'(t) dt, where g(t) = y and f(t) = x

The Attempt at a Solution


I believe that the limits of integration by be found by setting x and y equal to each other and solving for y. Do I still use the given equation, or do I have to modify it as this question asks about the y-axis, not the x-axis.

Thanks
The limits of integration are the values of t where your curve intersects the y-axis. The y-axis is where the value of x equals 0. Solve that.
 
  • #3
297
6
I solved t^2 - 2t = x = 0 and I got t = 2 and t = 0, so those are my limits
Now, do I still use ∫g(t) f'(t) dt or do I have to modify the equation to ∫f(t) g'(t) dt ?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
I solved t^2 - 2t = x = 0 and I got t = 2 and t = 0, so those are my limits
Now, do I still use ∫g(t) f'(t) dt or do I have to modify the equation to ∫f(t) g'(t) dt ?
You can actually use either one. One will give you the negative of the other. You can see this by looking at integration by parts.
 

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