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Math Help - Four questions need help on!

  1. #1
    Newbie
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    Mar 2008
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    Four questions need help on!

    I have four questions to ask.


    First:

    Use (a) the Trapezoid Rule, (b) the Midpoint Rule, and (c) Simpsonís Rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.

    ∫_0^1▒ √(1+ √x) dx,n=8

    Sorry don't know of to get the numbers ont he integral. the o is on bottm on and the one is on top

    same for the integral in the question below. and the rest below.

    Second:

    (a) Find the approximate T8 and M8 for ∫_0^1▒ cos⁡(x^2 )dx.
    (b) Estimate the errors involved in the approximations of part (a)
    (c) How large do we have to choose n so that the approximations Tn and Mn to the integral in part (a) are accurate to within 0.00001?

    Third:

    Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

    ∫_0^1▒ ln x/√x dx


    Fourth:

    Use the Comparison Theorem to determine whether the integral is convergent or divergent.

    ∫_1^∞▒ x/√(1+x^6 ) dx




    Well thats it.


    Sorry about the integral problems.
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  2. #2
    Grand Panjandrum
    Joined
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    4
    Quote Originally Posted by jconfer View Post
    I have four questions to ask.


    First:

    Use (a) the Trapezoid Rule, (b) the Midpoint Rule, and (c) Simpsonís Rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.

    ∫_0^1▒ √(1+ √x) dx,n=8

    Sorry don't know of to get the numbers ont he integral. the o is on bottm on and the one is on top

    same for the integral in the question below. and the rest below.

    Second:

    (a) Find the approximate T8 and M8 for ∫_0^1▒ cos⁡(x^2 )dx.
    (b) Estimate the errors involved in the approximations of part (a)
    (c) How large do we have to choose n so that the approximations Tn and Mn to the integral in part (a) are accurate to within 0.00001?

    Third:

    Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

    ∫_0^1▒ ln x/√x dx


    Fourth:

    Use the Comparison Theorem to determine whether the integral is convergent or divergent.

    ∫_1^∞▒ x/√(1+x^6 ) dx




    Well thats it.


    Sorry about the integral problems.
    Please post one question per thread, it simplifies the thread structure and
    makes it more likely you will recieve help.

    RonL
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