SOLUTION: Find the area enclosed by the curve x=t^2 - 2t, y=sqrt(t) and the y-axis.

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Question 988657: Find the area enclosed by the curve x=t^2 - 2t, y=sqrt(t) and the y-axis.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area enclosed by the curve x=t^2 - 2t, y=sqrt(t) and the y-axis.
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Eliminate t
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x=t^2 - 2t
y=sqrt(t) --> t = y^2
x = y^4 - 2y^2
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The area is the same as y = x^4 - 2x^2 and the x-axis
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Find the 2 x-intercepts:
x = 0 is one.
x%5E2+-+2+=+0
--> x+=+sqrt%282%29
=================-
INT(x^4 - 2x^2) = x^5/5 - 2x^3/3
Area = |%28sqrt%282%29%29%5E5%2F5+-+2%28sqrt%282%29%29%5E3%2F3|
=~ 0.754247 sq units