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Math Help - Evaluating trig function

  1. #1
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    Evaluating trig function

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

    Attempt to solution:

     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 \int_2^4
    . . . . . . and l use the following substitution:  x\:=\:2\sec\theta .

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

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

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

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

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

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