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Math Help - Integral help

  1. #1
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    Integral help

    Im having trouble solving these intergrals...if anyone can help thatd be great,
    Compute the integral from -1 to 3 of the square root of (6-2x^2+4x) dx..

    Also, evaluate the indefinate integral of dx / square root of (1-x^2+2x)

    I know where to start, but i keep getting stuck where i have to take the antiderivative of ax^-1..which would be x^0 which doesnt make sence...
    Thanks in advance
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  2. #2
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    Quote Originally Posted by shmayer View Post
    Im having trouble solving these intergrals...if anyone can help thatd be great,
    Compute the integral from -1 to 3 of the square root of (6-2x^2+4x) dx..

    Also, evaluate the indefinate integral of dx / square root of (1-x^2+2x)

    I know where to start, but i keep getting stuck where i have to take the antiderivative of ax^-1..which would be x^0 which doesnt make sence...
    Thanks in advance
    \int \sqrt{6-2x^2+4x} \, dx

    \int \sqrt{8 - 2(x^2 - 2x + 1)} \, dx

    \int \sqrt{8 - 2(x-1)^2} \, dx

    now use the trig substitution x-1 = 2\sin{t}


    \int \frac{1}{\sqrt{1-x^2+2x}} \, dx

    \int \frac{1}{\sqrt{2 - (x^2-2x+1)}} \, dx

    \int \frac{1}{\sqrt{2 - (x-1)^2}} \, dx

    you should recognize this integral form's antiderivative as an arcsine function.
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