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Math Help - did i do these correctly?

  1. #1
    Senior Member
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    did i do these correctly?

    1) Find the area enclosed by the curves y=x^2 and y=x
    My answer: \frac{1}{6}



    2) Find the area bounded by the curves: x=-y^2 and x=-y-2
    My answer: \frac{-9}{2}




    3) Evaluate: \int \frac{2x}{(x^2+1)^3} dx


    My answer: \frac{-1}{2}(x^2+1)^{-2}+c



    4) Find the equation of the tangent line to y=sin(3x) where x=\pi
    My answer: y=-3(x-\pi)

    If any of my answers are incorrect then please let me know which one(s).
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by yoman360 View Post
    1) Find the area enclosed by the curves y=x^2 and y=x
    My answer: \frac{1}{6}



    2) Find the area bounded by the curves: x=-y^2 and x=-y-2
    My answer: \frac{-9}{2}




    3) Evaluate: \int \frac{2x}{(x^2+1)^3} dx


    My answer: \frac{-1}{2}(x^2+1)^{-2}+c



    4) Find the equation of the tangent line to y=sin(3x) where x=\pi
    My answer: y=-3(x-\pi)

    If any of my answers are incorrect then please let me know which one(s).
    1, 3, and 4 look okay. Not sure about 2. If they are asking for area, it should be a positive amount.
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  3. #3
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    #2. The answer should be 9/2. You should integrate -y^2 + y + 2 and your bounds for integration are -1 and 2. Doing so will lead to a positive value 9/2
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