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Integral draw a line problem

  1. Jan 22, 2005 #1
    [tex]\int_1^{13} f(x) - \int_1^{10} f(x) = \int_a^{b} f(x)[/tex]

    Question:

    where a = ____ and b = ____

    what is it asking me extactly? is it just telling me to substract the b's and a's? if so, a = 0 and b = 3, but it's wrong.
     
  2. jcsd
  3. Jan 22, 2005 #2

    BobG

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    Draw f(x) on a graph (it doesn't really matter what f(x) is, just draw a curvy line from 0 to 13). Draw a vertical line from x=1 to the curve. Draw a vertical line from 10 to the curve. Draw a vertical line from 13 to the curve.

    Your first integral is the area under the curve from 1 to 13. The second integral subtracts the area under the curve from 1 to 10 (shade it in). What are you left with. This is the area you want to calculate.

    You're right you have an interval of 3, but unless f(x) is a straight horizontal line, the area from 10 to 13 won't necessarily be the same as the area from 0 to 3.
     
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