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Thread: Find the MacLaurin polynomial of degree 5 for F(x).

  1. #1
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    Find the MacLaurin polynomial of degree 5 for F(x).

    Let .
    Find the MacLaurin polynomial of degree 5 for .

    Use this polynomial to estimate the value of .
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  2. #2
    Bop
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    Hello, just solve the integral and apply MacLaurin series. And in order to calculate the define integral just replace the values.
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  3. #3
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    Don't solve the integral (it cannot be done in terms of elementary functions, anyway)! You only need the value of F at x= 0 which is obviously 0 because \int_0^0 f(x)dx= 0 for any f.

    Then use the Fundamental Theorem of Calculus to find F'(x) and differentiate that to get F", F''', F'''', and F'''''.
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  4. #4
    Bop
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    I hadn't seen it was function of x, my mistake.
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