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Thread: Evaluating trig function

  1. #1
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    Evaluating trig function

    My original integral has the following limits $\displaystyle \int_2^4$ and l use the following substitution $\displaystyle x=2sec\theta $. My question is how do l change the limits of the integral ?

    Attempt to solution:

    $\displaystyle x=2sec(2) $

    x=2cos1\2

    Is this correct ?
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  2. #2
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    Hello, nyasha!

    My original integral has the following limits $\displaystyle \int_2^4$
    . . . . . . and l use the following substitution: $\displaystyle x\:=\:2\sec\theta $.

    My question is: How do l change the limits of the integral ?

    Note that the limits are for $\displaystyle {\color{blue}x}\!:\;\;\int^{x=4}_{x=2}f(x)\,dx$

    For the upper limit, $\displaystyle x = 4$, we have:.$\displaystyle 4 \:=\:2\sec\theta \quad\Rightarrow\quad \sec\theta \:=\:2\quad\Rightarrow\quad \theta \:=\:\frac{\pi}{3}$

    For the lower limit, $\displaystyle x = 2$, we have: .$\displaystyle 2 \:=\:2\sec\theta \quad\Rightarrow\quad \sec\theta \:=\:1 \quad\Rightarrow\quad \theta \:=\:0$

    So your integral becomes: .$\displaystyle \int^{\frac{\pi}{3}}_0 g(\theta)\,d\theta $

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