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Math Help - Help with integration!

  1. #1
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    Help with integration!

    Hi

    I really need help with these two questions, for the first attachement I have no idea how to do that last part circled in pink

    For the second attachement(labeled part e.)), I could not get the answer - I got \frac{4sqrt{2}}{sqrt{3}}arctan(\frac{sqrt{2}}{sqrt  {3}}) + c but the answer is \2\frac{sqrt{2}}{sqrt{3}}arctan(\frac{sqrt{2}}{sqr  t{3}}) + c

    Thank you so much in advance!
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  2. #2
    Junior Member FelixFelicis28's Avatar
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    Re: Help with integration!

    Quote Originally Posted by Tutu View Post
    Hi

    I really need help with these two questions, for the first attachement I have no idea how to do that last part circled in pink

    For the second attachement(labeled part e.)), I could not get the answer - I got \frac{4sqrt{2}}{sqrt{3}}arctan(\frac{sqrt{2}}{sqrt  {3}}) + c but the answer is \2\frac{sqrt{2}}{sqrt{3}}arctan(\frac{sqrt{2}}{sqr  t{3}}) + c

    Thank you so much in advance!
    1) You have \int_0^3 f(x) \ dx = 8 = \int_c^d f(x-2) \ dx

    Integration by substitution - the substitution should be pretty easy to spot, bearing in mind the argument of f(x-2).

    2) Their answer is correct, I cannot point out what you've done incorrectly unless you post your working OP, likely a small arithmetical error somewhere.
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    Re: Help with integration!

    Hi thank you so much!

    For the second, attached is my working, I had simply used the formula so its sort of one step..can you help me see where I went wrong?
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  4. #4
    Junior Member FelixFelicis28's Avatar
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    Re: Help with integration!

    Quote Originally Posted by Tutu View Post
    Hi thank you so much!

    For the second, attached is my working, I had simply used the formula so its sort of one step..can you help me see where I went wrong?
    You haven't done \int \frac{dx}{a^2 + (px+q)^2} = \frac{1}{ap} \arctan \left(\frac{px+q}{a}\right) + \mathcal{C}

    but rather:

    \int \frac{dx}{a^2 + (px+q)^2} = \frac{1}{a} \arctan \left(\frac{px+q}{a}\right) + \mathcal{C}.
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    Re: Help with integration!

    Help with integration!-23-sep-13.png
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