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Math Help - More integrals

  1. #1
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    More integrals

    Evaluate the integral.. x -1/ sqrt x dx at interval (1,9)
    Evaluate the integral x(3sqrtx + 4sqrtx)
    Evaluate the integral 1 + cosx/cosx r4om interval (0, pi/4)
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    Quote Originally Posted by Jgirl689 View Post
    Evaluate the integral.. x -1/ sqrt x dx at interval (1,9)
    Evaluate the integral x(3sqrtx + 4sqrtx)
    Evaluate the integral 1 + cosx/cosx r4om interval (0, pi/4)
    \int{x(3\sqrt{x} + 4\sqrt{x})\,dx} = \int{7x^{\frac{3}{2}}\,dx}

     = \frac{14}{5}x^{\frac{5}{2}} + C

     = \frac{14\sqrt{x^5}}{5} + C.


    With the rest, you'll need to put brackets where they're needed. They're too hard to read.
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  3. #3
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    Quote Originally Posted by Jgirl689 View Post
    Evaluate the integral.. x -1/ sqrt x dx at interval (1,9)
    Evaluate the integral x(3sqrtx + 4sqrtx)
    Evaluate the integral 1 + cosx/cosx r4om interval (0, pi/4)
    1. (x-1)/(sqrt x) from interval (1,9)
    2. (1+cosx)/(cosx) from interval (0, pie/4)
    By the way, the other one posted is supposed to be (sqrt x ^3 + sqrt x ^4)..3 and 4 are roots..
    Last edited by Jgirl689; February 23rd 2010 at 09:13 PM.
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  4. #4
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    Quote Originally Posted by Jgirl689 View Post
    Evaluate the integral.. x -1/ sqrt x dx at interval (1,9)
    Evaluate the integral x(3sqrtx + 4sqrtx)
    Evaluate the integral 1 + cosx/cosx r4om interval (0, pi/4)
    To check answers (and perhaps even get solutions) use Wolfram|Alpha
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  5. #5
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    Thanks but none of them show how the steps are done, some do even show for integrals ...someone please help me on these!
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    Quote Originally Posted by Jgirl689 View Post
    Thanks but none of them show how the steps are done, some do even show for integrals ...someone please help me on these!
    For 1st and 3rd,

    Use:

    \frac{a \pm b}{c}=\frac{a}{c} \pm \frac{b}{c} for  c \neq 0.
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  7. #7
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    Quote Originally Posted by Jgirl689 View Post
    1. (x-1)/(sqrt x) from interval (1,9)
    2. (1+cosx)/(cosx) from interval (0, pie/4)
    By the way, the other one posted is supposed to be (sqrt x ^3 + sqrt x ^4)..3 and 4 are roots..
    \int{\frac{x - 1}{\sqrt{x}}\,dx} = \int{(x - 1)x^{-\frac{1}{2}}\,dx}

     = \int{x^{\frac{1}{2}} - x^{-\frac{1}{2}}\,dx}.

    Now apply the power rule.



    \int{\frac{1 + \cos{x}}{\cos{x}}\,dx} = \int{(1 + \cos{x})\sec{x}\,dx}

     = \int{\sec{x} + 1\,dx}.

    You should be able to go from here.



    I assume for the other one, you mean

    \int{x(\sqrt[3]{x} + \sqrt[4]{x})\,dx} = \int{x(x^{\frac{1}{3}} + x^{\frac{1}{4}})\,dx}

     = \int{x^{\frac{4}{3}} + x^{\frac{5}{4}}\,dx}.

    Now use the power rule.
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