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Math Help - Transforming trigonometric integrands

  1. #1
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    Transforming trigonometric integrands

    Hi,

    I am having trouble at transforming trigonometric integrands. I just need these to be transformed then I think I will be able to integrate it. I hope you can help me.



    Thank you.
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    Re: Transforming trigonometric integrands

    Quote Originally Posted by reiward View Post
    Hi,

    I am having trouble at transforming trigonometric integrands. I just need these to be transformed then I think I will be able to integrate it. I hope you can help me.



    Thank you.
    \displaystyle \begin{align*} \int{\frac{3\cos{x} - 4}{\sin^2{x}}\,dx} &= \int{\frac{3\cos{x}}{\sin^2{x}}\,dx} - \int{\frac{4}{\sin^2{x}}\,dx} \\ &= \int{\frac{3\cos{x}}{\sin^2{x}}\,dx} - \int{4\csc^2{x}\,dx}\end{align*}

    Solve the first using the substitution \displaystyle \begin{align*}  u = \sin{x} \implies du = \cos{x}\,dx \end{align*} and for the second, what is the derivative of \displaystyle \begin{align*} \cot{x} \end{align*} ?
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    Re: Transforming trigonometric integrands

    Quote Originally Posted by reiward View Post
    Hi,

    I am having trouble at transforming trigonometric integrands. I just need these to be transformed then I think I will be able to integrate it. I hope you can help me.



    Thank you.
    \displaystyle \begin{align*} \int{\left(3 - \csc^2{y}\right)\cos{y}\,dy} &= \int{\left(3 - \frac{1}{\sin^2{y}}\right)\cos{y}\,dy} \end{align*}

    Now make the substitution \displaystyle \begin{align*} u = \sin{y} \implies du = \cos{y}\,dy \end{align*} .
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