jocelynevsq
find the region bounded by the graph of y^2=x^2-x^4
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amistre64
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what does your graph look like?
jocelynevsq
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|dw:1359922854861:dw|
jocelynevsq
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i'm not sure
jocelynevsq
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wait nevermind it's not that
amistre64
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|dw:1359922919356:dw|
thats what i was thinking it was like
jocelynevsq
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yes
amistre64
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then the only pertinent equations are:
x^2-x^4 and y=-sqrt(x)
amistre64
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they meet at x=0, and what is the other x value?
jocelynevsq
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I don't know
amistre64
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-sqrt(x) = x^2 - x^4
0 = x^2 -sqrt(x) -x^4
that does seem a bit convoluted :/
ZeHanz
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Here's the graph:
amistre64
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hmmm, that is one representation i can see of it :)
amistre64
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so if thats the case, would changing it to parametric form help out?
ZeHanz
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I'd:
Write y as function of x: y=xsqrt(1-x²)
Integrate using u=1-x²
Multiply by 4, because of the symmetry...
amistre64
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sounds crazy enough to work :)
jocelynevsq
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what do I multiply by 4?
ZeHanz
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If you integrate as I did, you only get the area between the positive x-axis and the graph (upper right part of the whole thing) There a 4 such areas, so multiply by 4.
jocelynevsq
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oh okay thanks
ZeHanz
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I've got to 8/3, hope this helps ;)
jocelynevsq
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thanks!