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Math Help - exponential integral problem

  1. #1
    Junior Member
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    exponential integral problem

    What is the integral from -2 to 2 of (3u+1)^2 du?

    Here is my work so far:

    ((3u+1)^3)/3

    ((3(2)+1)^3)/3 - ((3(-2)+1)^3)/3

    = 343/3 + 125/3

    = 468/3

    = 156

    I know that is wrong but the book says it is 52. I realized if I divide my final answer again I will get it so I was thinking that I multiplied by 3 one time too many or something. That or I made an error somewhere else.

    Thanks for the help in advance.
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  2. #2
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    You forgot something. If you were to sub z = 3u+1 \implies dz = 3~du, the integral becomes:

    \frac{1}{3}\int z^2~du = \frac{z^3}{9} + C

    Now evaluate the definite integral.

    Of course, this can be tackled very easily without resorting to subs. But I had to use it here for clarity.
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  3. #3
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    Excuse me if you don't understand me, but this is my first time posting on these forums.

    Your problem is finding your anti-derivative. To check yourself, try taking the derivative back. If you use the chain rule correctly, you will see that it is 3 times more than you wanted. So to fix this, just divide by another 3. this will leave you with

    ((3u+1)^3)/9. From here, just plug in your numbers(2 and -2)

    When you plug them in you get 343/9 + 125/9. which equals 52.

    Hope this helped,

    -Equals
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  4. #4
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    Hey thanks for the input Chop Suey and Equals. Yeah I forgot to balance it out with the 1/3 on the outside. One of those slap your forehead "oh duh!" things.
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