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anneflys
Group Title
Find the area of the region bounded by the curves y=x^2 and y=x^4
 one year ago
 one year ago
anneflys Group Title
Find the area of the region bounded by the curves y=x^2 and y=x^4
 one year ago
 one year ago

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RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
1. find the intercept of the curve \[x^4  x^2 =0\]\[x^2 (x^21)=0\]\[x=0, 1, 1\] Then integrate it \[\int_{1}^{0}(x^2x^4)dx + \int_0^1(x^2x^4)dx\]
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
Or... since it is an even function, \[\int_{1}^{0}(x^2x^4)dx + \int_0^1(x^2x^4)dx\]\[=2\int_{1}^{0}(x^2x^4)dx\]
 one year ago

anneflys Group TitleBest ResponseYou've already chosen the best response.0
Wait, so why did you multiply everything by 2?
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
I didn't multiply everything by two... It's just \[\int_{1}^{0}(x^2x^4)dx = \int_0^1(x^2x^4)dx\] (Since it is an even function) So, \[\int_{1}^{0}(x^2x^4)dx + \int_0^1(x^2x^4)dx\]\[=\int_{1}^{0}(x^2x^4)dx +\int_{1}^{0}(x^2x^4)dx \]\[=2\int_{1}^{0}(x^2x^4)dx \]Using the property of even function can save some work.
 one year ago
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