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Quick question on integral calculation

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data
    Hello, I have a question from my textbook on integral calculation. It's
    Find f(pi/2) from the following information.
    (i) f is positive and continuous.
    (ii) the area under the curve y=f(x) from x=0 to x=a is a2+(a/2)*sin(a)+(π/2 )*cosa

    So I think the second condition implies
    F(a)-F(0) = a2+(a/2)*sin(a)+(π/2 )*cosa (F is the antiderivate of f)
    But if I let a=0, I find the lefthand side of the equation will be 0 but the righthand side will be π/2 .
    So please someone tell me where I made a mistake which seems to be quite a silly one.
    Thanks in advance.


    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 3, 2011 #2
    Did you calculate the derivative?
     
  4. Oct 3, 2011 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Either you copied the question incorrectly or else the book has written an incorrect question. You are right: the two sides are different in the limit a-->0.

    RGV
     
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