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Math Help - Evaluate the following integrals please

  1. #1
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    Evaluate the following integrals please

    hello, can someone help me these questions?


    a) {{{ int ( lnt/sqrt(t), dt, 4, 9) }}}
    b) {{{ int ( cos(sqrt(6x)), dx ) }}}
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  2. #2
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    Quote Originally Posted by yeeho View Post

    a) {{{ int ( lnt/sqrt(t), dt, 4, 9) }}}
    For \int \frac{\ln t}{\sqrt{t}}~dt

    By parts, make \displaystyle v = \ln t , \frac{du}{dt} = \frac{1}{\sqrt{t}}


    Quote Originally Posted by yeeho View Post

    b) {{{ int ( cos(sqrt(6x)), dx ) }}}
    For this one sub t = \sqrt{x} then integrate by parts.
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  3. #3
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    One way of stating the formula for integration by parts is:

    \displaystyle \int_a^b f'(x)g(x)\;{dx} = g(x)\cdot f(x)\bigg|_{a}^{b}-\int_a^b f(x)g'(x)\;{dx}

    Therefore (without defining new variables) we can write the integral as:

    \displaystyle \int_4^9 \frac{\ln{t}}{\sqrt{t}}\;{dt} = 2\int_4^9 (\sqrt{t})'\ln{t}}\;{dt} = 2\sqrt{t}\ln{t}\bigg|_4^9-2\int (\ln{t})'\sqrt{t}\;{dt}
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