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Confusing Error in Should-Be-Simple Integration Problem

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Find k such that the area between the function and the x-axis, bounded by x = 1 and x = k, is equal to 100 square units.

    2. Relevant equations

    y = 4e^(x/5)

    3. The attempt at a solution

    1. Wrote the problem as the definite integral from 1 to k of 4e^(x/5)dx = 100.

    2. Antidifferentiated to obtain 20e^(x/5).

    3. Made substitutions into F(b) - F(a) = 100 to obtain 20e^(k/5) - 20e^(1/5) = 100.

    4. Solved for k and got k = 5*ln(5) + 1.

    5. At that point I thought I had it all figured out, but when I did 20e^((5*ln(5) + 1)/5) - 20e^(1/5) to check I get 97.7122207 as the result. What am I doing wrong here? Any help would be appreciated.
     
  2. jcsd
  3. Aug 23, 2011 #2

    diazona

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    Homework Helper

    Check your math going from step 3 to step 4. You should be getting a slightly different result for k.
     
  4. Aug 23, 2011 #3
    Righto, found out what I was doing wrong: I somehow forgot that logs don't distribute over multiplication. How silly of me.

    k = 5*ln(5 + e^(1/5))

    Edit: Thanks for the help.
     
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