Question 988657
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^2 - 2 = 0}}}
--> {{{x = sqrt(2)}}}
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INT(x^4 - 2x^2) = x^5/5 - 2x^3/3
Area = |{{{(sqrt(2))^5/5 - 2(sqrt(2))^3/3}}}|
=~ 0.754247 sq units