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Math Help - Area between Curves

  1. #1
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    Area between Curves

    I want to find the area between the curves y=12-x^2 and y=x^2-6. If you graph these functions, you can see they intersect at (-3,3) and (3,3). The graph is also symmetric about the y-axis, so I will find the area by finding the area of the left side, and mulitplying it by two. I will chop the left hand side, into two areas A_1 and A_2 where A_1=\int_{3}^{12}\sqrt{12-y}dy and A_2=\int_{-6}^{3}\sqrt{y+6}dy. The total area will be:

    A=2(A_1+A_2)

    =2\left(\int_{3}^{12}\sqrt{12-y}dy+\int_{-6}^{3}\sqrt{y+6}dy\right)

    Am I setting this up right?
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  2. #2
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    Quote Originally Posted by adkinsjr View Post
    I want to find the area between the curves y=12-x^2 and y=x^2-6. If you graph these functions, you can see they intersect at (-3,3) and (3,3). The graph is also symmetric about the y-axis, so I will find the area by finding the area of the left side, and mulitplying it by two. I will chop the left hand side, into two areas A_1 and A_2 where A_1=\int_{3}^{12}\sqrt{12-y}dy and A_2=\int_{-6}^{3}\sqrt{y+6}dy. The total area will be:

    A=2(A_1+A_2)

    =2\left(\int_{3}^{12}\sqrt{12-y}dy+\int_{-6}^{3}\sqrt{y+6}dy\right)

    Am I setting this up right?

    finding the area w/r to x is much easier ...

    A = 2 \int_0^3 (12-x^2) - (x^2-6) \, dx
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