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Thread: Integral (finished--need someone to check!)

  1. #1
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    Integral (finished--need someone to check!)

    the integral is from 0 to π/4:

    (1 + tanθ)^3(sec^2θ)dθ

    So, here's what I did:

    u = 1 + tanθ
    du = sec^2θdθ

    so,

    (u)^3du

    then, I changed the integral limits because I think I'm supposed to (not sure?)

    1 + tanθ(π/4) = 2
    1 + tanθ(0) = 1

    so,

    1/4(u)^4

    then I simply plugged the new limit numbers into the equation to finish it

    [1/4(2)^4] - [1/4(1)^4] = 15/4

    Did I do it right?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by OhhCalculus View Post
    the integral is from 0 to π/4:

    (1 + tanθ)^3(sec^2θ)dθ

    So, here's what I did:

    u = 1 + tanθ
    du = sec^2θdθ

    so,

    (u)^3du

    then, I changed the integral limits because I think I'm supposed to (not sure?)

    1 + tanθ(π/4) = 2
    1 + tanθ(0) = 1

    so,

    1/4(u)^4

    then I simply plugged the new limit numbers into the equation to finish it

    [1/4(2)^4] - [1/4(1)^4] = 15/4

    Did I do it right?
    Seems right to me.
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  3. #3
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    pickslides's Avatar
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    Does this give you the same answer?

    $\displaystyle \displaystyle \left[ \frac{1}{4}(\tan \theta+1)^4\right]_0^{\frac{\pi}{4}}$
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  4. #4
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    Quote Originally Posted by OhhCalculus View Post
    the integral is from 0 to π/4:

    (1 + tanθ)^3(sec^2θ)dθ

    So, here's what I did:

    u = 1 + tanθ
    du = sec^2θdθ

    so,

    (u)^3du
    Execellent!

    then, I changed the integral limits because I think I'm supposed to (not sure?)
    You could either
    1) Do the integral in terms of u, then write the answer in terms of $\displaystyle \theta$ again and evaluate between the limits of the original integral.
    2) change the limits of integration to values of u and then evaluate the between those limits.

    In my opinion, it is better and easier to do (2) as you do here.
    Of course, you do NOT use the "$\displaystyle \theta$" values with the "u" variable!

    1 + tanθ(π/4) = 2
    1 + tanθ(0) = 1

    so,

    1/4(u)^4

    then I simply plugged the new limit numbers into the equation to finish it

    [1/4(2)^4] - [1/4(1)^4] = 15/4

    Did I do it right?
    Follow Math Help Forum on Facebook and Google+

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