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Math Help - Integrals and Sigma

  1. #1
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    Integrals and Sigma

    Hello I need help with 2 problems.

    The first is
    Code:
    F(x)= Integral from sqrt(x) to 2  (tan(t)/t^2) dt     Find F'(x)

    The second is
    Code:
    Find the actual area under the curve f(x)=2x^2 on the interval [0,3]. Use right hand endpoints and the formula
    Area = lim n ∞   n Σ i=1    f(x^*i) delta(x)

    Here is an image of the equations
    Integrals and Sigma-photo.jpg
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  2. #2
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    Re: Integrals and Sigma

    For the first part, I would perform the following transformation:

    \displaystyle \begin{align*} \int_2^{\sqrt{x}}{\frac{\tan{(t)}}{t^2}\,dt} &= \frac{1}{2}\int_2^{\sqrt{x}}{\frac{2t\tan{(t)}}{t^  3}\,dt} \end{align*}

    Let \displaystyle \begin{align*} u = t^2 \implies du = 2t\,dt \end{align*} and changing the bounds gives

    \displaystyle \begin{align*} \frac{1}{2} \int_4^x { \frac{ \tan{ \left( \sqrt{u} \right) } }{ u^{\frac{3}{2}} }\,du } \end{align*}

    Then you can make use of the Second Fundamental Theorem of Calculus.

    For the second, you have been given a formula to use. Where exactly are you stuck?
    Last edited by Prove It; December 3rd 2012 at 07:30 PM.
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  3. #3
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    Re: Integrals and Sigma

    Okay thanks ill take another look at the first problem and for the second problem the equation confuses me. What does the x*i mean?
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  4. #4
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    Re: Integrals and Sigma

    \displaystyle \begin{align*} x^*_i \end{align*} is just a shorthand to give a label to each value of x.
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  5. #5
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    Re: Integrals and Sigma

    Okay I get problem 2 all the way up to this point

    Integrals and Sigma-photo-1-.jpg

    What is the n^3/3 + ...
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