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Math Help - Area bounded by y=4 and 4/(1+x^2)

  1. #1
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    Area bounded by y=4 and 4/(1+x^2)

    The question asks for the area bounded by y=4 and 4/(1+x^2) from x=-1 to x=1.
    I used definition integral to do this question and get (4x - 4*arctan(x)) from x=-1 to x=1.
    However, when I plug in the numbers, I don't know which value to use for arctan(-1). If I use arctan(-1) = 3 pi/4, I would get an answer from the answer key. (The answer key says arctan(-1) = -pi/4.

    How do I know which value I should use?
    Please help me! Thanks!
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  2. #2
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    Re: Area bounded by y=4 and 4/(1+x^2)

    Hey LLLLLL.

    You should use the principal branch which means answers lie in the range [-pi/2,pi/2] if you include -infinity and +infinity.
    Thanks from LLLLLL
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  3. #3
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    Re: Area bounded by y=4 and 4/(1+x^2)

    Quote Originally Posted by chiro View Post
    Hey LLLLLL.

    You should use the principal branch which means answers lie in the range [-pi/2,pi/2] if you include -infinity and +infinity.
    Oh my! I totally forgot to check the thread!
    Thank you so much for helping me!!
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