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Thread: substitution

  1. #1
    Junior Member
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    substitution

    use substitution method

    1. integral (sec^2[x]/tan[x]
    2.integral (0 to pi/2) sin(x)cos^2(x)
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  2. #2
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    Hello, Gracy!

    Use substitution method

    $\displaystyle 1)\;\int \sec^2\!x\tan x\,dx$

    We have: .$\displaystyle \int \sec x\,(\sec x\tan x\,dx)$

    Let $\displaystyle u = \sec x$


    $\displaystyle 2)\;\int^{\frac{\pi}{2}}_0 \sin x \cos^2\!x \,dx$

    We have: .$\displaystyle \int^{\frac{\pi}{2}}_0\cos^2\!x\,(\sin x\,dx)$

    Let $\displaystyle u = \cos x$

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