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Math Help - Definite integrals.

  1. #1
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    Definite integrals.

    i need help with these problems please?:

    (bSa is the intergration symbol with the a and b values)

    1S0 36dx/(2x+1)^3


    (pi)/2S0 5sin^(3/2)xcosxdx


    (pi)/4S0 e^(tanx)sec^2xdx
    Last edited by mr fantastic; January 3rd 2011 at 09:52 PM. Reason: Re-titled.
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    Quote Originally Posted by zdawg View Post
    1S0 36dx/(2x+1)^3
    Just clarifying \displaystyle\int_0^1 \frac{36}{(2x+1)^3}~dx ?, if so use a substitution \displaystyle u= 2x+1
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    yeah, thats what i ment, sorry.
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    Well as I pointed out \displaystyle\int_0^1 \frac{36}{(2x+1)^3}~dx

    Make \displaystyle u= 2x+1\implies \frac{du}{dx} = 2

    Giving \displaystyle\int_0^1 \frac{2\times 18}{(2x+1)^3}~dx = \int_1^3 \frac{ 18}{(u)^3}~du= 18\int_1^3 \frac{ du}{(u)^3}
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    my txtbk says the final answer is 8, do you know how to get there?
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    Quote Originally Posted by zdawg View Post
    my txtbk says the final answer is 8, do you know how to get there?
    I do, by completeing the hints given in post #4. Can you finish it using simple integration?
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  7. #7
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    Quote Originally Posted by zdawg View Post
    [snip]

    (pi)/2S0 5sin^(3/2)xcosxdx


    (pi)/4S0 e^(tanx)sec^2xdx
    (b) Substitute u = \sin (x).

    (c) Substitute u = \tan (x).

    If you need more help, post what you can do and make it clear where you get stuck.
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