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Math Help - find the area of the region

  1. #1
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    find the area of the region

    scetch the reason enclosed by x+y2=42 and x+y=0 Decide whether to integrate with respect to x or y. Then find the area of the region.

    i tried solving for x but all i get is 7 can someone help im not sure how to integrate if i only get 1 point
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  2. #2
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    Krizalid's Avatar
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    We clearly need to integrate w.r.t. y, so let's solve 42-y^2=-y\implies y^2-y-42=(y+6)(y-7)=0, so we integrate for -6\le y\le7. Now put f(y)=42-y^2 and g(y)=-y and see that it's f(y)\ge g(y) and the integral which gives the area is \int_{-6}^7\big(f(y)-g(y)\big)\,dy.
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