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Math Help - Check answer for this difinate integral

  1. #1
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    Check answer for this difinate integral

    Hi,

    Could someone please check the answer for this?
    I keep coming up with an answer of 32/225. However the answer sheet has it as 16/225.

    The question is evaluate the integral of 4/(1+2t)^3 on the interval of [1,2]
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Craka View Post
    Hi,

    Could someone please check the answer for this?
    I keep coming up with an answer of 32/225. However the answer sheet has it as 16/225.

    The question is evaluate the integral of 4/(1+2t)^3 on the interval of [1,2]
    \int_1^{2}\frac{4}{(1+2t)}dt=2\int_1^{2}\frac{2}{(  1+2t)^3}=2\bigg[\frac{-1}{2(1+2t)^2}\bigg]\bigg|_1^{2}=\frac{16}{225}
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  3. #3
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    Do you pull the 2 out to the front of the integral due to it being a derivative of 1+2t and also a factor of the numerator?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Craka View Post
    Do you pull the 2 out to the front of the integral due to it being a derivative of 1+2t and also a factor of the numerator?
    Yes, I pulled the 2 our solely to accentuate the derivative of the quantity 1+2t being in the numerator, it is not neccasary
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