Help with Area of parametric equations problem

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Homework Help Overview

The problem involves finding the area of a region enclosed by a set of parametric equations defined as x=t^3-8t and y=2t^2. The original poster expresses uncertainty about how to begin solving the problem, particularly regarding the manipulation of the equations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need for additional information regarding how the region is enclosed, with some suggesting it may involve the x-axis. The original poster questions the clarity of the problem statement and the feasibility of solving for t. Others mention graphing the equations to visualize the curve and identify the bounds for t.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the use of integrals to find the area, but there is no explicit consensus on the approach or the necessary information to proceed.

Contextual Notes

Participants note the lack of clarity in the problem statement, particularly regarding the enclosure of the region and the bounds for t. There is an acknowledgment of potential missing information that could aid in solving the problem.

Mcbrown108
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Homework Statement



Find the area of the region enclosed by the parametric equation
x=t^3-8t
y=2t^2





The Attempt at a Solution


I am not even sure how to start this problem.
I read somewhere that to start with you solve for t in one of the equations.
when i solve for t I end up with really weird equations.

Can anyone help?
 
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There must be more information, does it say how the region is enclosed? I'm assuming it's with the x axis. Always be sure to include all the information in the question.
 
That is all that is given to me. I thought I was missing some information as well.
 
Oh, that's really, really weird! I was all set to agree with gamesguru but, just to make sure, I graphed it on my TI-83. That is a closed curve with t going from [itex]-\sqrt{8}[/itex] to [itex]\sqrt{8}[/itex].

You should be able to find the area by using the fact that
[tex]\int y(x)dx= \int y(t)\frac{dx}{dt}dt[/tex]
 
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