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Math Help - Is this correct? solving integrals

  1. #1
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    Is this correct? solving integrals

    Question:
    ∫dt/(cos^2tsqarrt(1+tant)

    Mywork:
    sqrt(1+tan(t)) = (1+tan(t))^(1/2)
    let u = (1+tan(t))^(1/2)
    du = (1/2) (1+tan(t))^(-1/2) sec^2(t) dt
    du = 1/2 (1+tan^2(t))^(1/2) cos^2(t) dt
    du = 1/2 sqrt(1+tan^2(t)) cos^2(t) dt
    The given integral becomes
    2∫ du
    =2u + C
    = 2sqrt(1+tan^2(t)) + C
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  2. #2
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    Quote Originally Posted by kensington View Post
    Question:
    ∫dt/(cos^2tsqarrt(1+tant)

    Mywork:
    sqrt(1+tan(t)) = (1+tan(t))^(1/2)
    let u = (1+tan(t))^(1/2)
    du = (1/2) (1+tan(t))^(-1/2) sec^2(t) dt
    du = 1/2 (1+tan^2(t))^(1/2) cos^2(t) dt
    Be careful here- you mean 1/2((1+ tan^2(t))^(1/2)(cos^2(t))) don't you?
    That is, \frac{1}{2(1+ tan^2(t))^{1/2}cos^2(t)} and not \frac{1}{2}(1+ tan^2(t))^{1/2} cos^2(t), which is what you wrote.

    du = 1/2 sqrt(1+tan^2(t)) cos^2(t) dt
    The given integral becomes
    2∫ du
    =2u + C
    = 2sqrt(1+tan^2(t)) + C
    With my comment, yes, that is correct.
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