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Math Help - The definite integral

  1. #1
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    The definite integral

    Substitute the limits correctly. The constant of integration is eliminated during subtraction.
    Attached Thumbnails Attached Thumbnails The definite integral-evaluate.bmp  
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  2. #2
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    Quote Originally Posted by norivea
    Substitute the limits correctly. The constant of integration is eliminated during subtraction.
    INT.(-1 --> 0)[(2-x)^4]dx

    if u = (2-x), then du = -dx, or dx = -du.
    So the original integral, in indefinite form, becomes
    INT.[u^4](-du)
    So, to continue,
    = (-)INT.[u^4]du
    = -(1/5)u^5 +C
    which is, when going back away from u,
    = -(1/5)(2-x)^5 +C
    Now we can use the original boundaries for the definite integration,
    = -(1/5)[(2-x)^5](-1 --> 0)
    = -(1/5)[(2 -0)^5] -{-(1/5)[(2 -(-1))^5]}
    = -(1/5)[2^5] +(1/5)[3^5]
    = -(1/5)[32] +(1/5)[243]
    = (1/5)[243 -32]
    = (1/5)[211]
    = 42.2 --------------answer.
    Last edited by ticbol; May 19th 2006 at 07:08 PM. Reason: an end }.
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