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CALCULUS HELP PLEASE!!

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Intergral from -2 to 2 (-2 is at the bottom of the integral sign and 2 is at the top) x^-2dx = -x^-1] (the bracket has a 2 at the top and -2 at the bottom) = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2) = -1

Is this true or false. I think it's false, but can someone explain to me why it's false.

  • CALCULUS HELP PLEASE!! -

    The question is done correctly.

    When you differentiate
    -x^-1 you get x^-2
    and all the arithmetic was done correctly.

    If this an "area between curves" type, I have seen this before.
    The function f(x) = 1/x^2 is discontinuous at x=0
    so even though calculation-wise we come up with the answer above, it would be meaningless.

  • CALCULUS HELP PLEASE!! -

    The answer is wrong because function x^(-2)>0 on [-2,2] except x=0 =>integral>0
    This is Improper integral which is divergent.

    x^(-1)-->infinity if x-->0

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