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

RolyPolyBest 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

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

RolyPolyBest 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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