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Thread: Definite integral of -cosx

  1. #1
    Dec 2008
    I live in the South-East of England

    Definite integral of -cosx

    The integral of -cosx is sinx. If I wish to define the interval between zero and pi to calculate the area of f(x) above and below the x-axis, I get:
    0 - 0 = 0.
    If I redefine the interval as 1/2pi to 3/2pi, I get 2 square units.
    But shifting the same interval up and down should not make any difference to the area of f(x) - but it does seem to!
    Can somebody tell me where I'm going wrong?
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  2. #2
    Dec 2008
    Dear John Brindley,

    the integral from a to b is not the area, but the signed area.

    integral -cos(x) from 0 to pi/2 = -1
    integral -cos(x) from pi/2 to pi = 1
    intergal from 0 to pi = (-1) + (+1) = 0.
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