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Math Help - Definite Integral help please

  1. #1
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    Definite Integral help please

    I'm having some problems figuring this out, should I do substitution and then integration by parts? or just substitution, I am a bit lost as to how to approach it and sadly our Friday quiz is going to look similar to this. any help is very appreciated , thank you!

    Integral (a= -pi/2, b=0) tan x sq.root(cos x) dx

    Sorry about problem presentation, don't know how to math tag sq. root or integral
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  2. #2
    Super Member PaulRS's Avatar
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    Try u=\cos(x)
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by bloomsgal8 View Post
    I'm having some problems figuring this out, should I do substitution and then integration by parts? or just substitution, I am a bit lost as to how to approach it and sadly our Friday quiz is going to look similar to this. any help is very appreciated , thank you!

    Integral (a= -pi/2, b=0) tan x sq.root(cos x) dx

    Sorry about problem presentation, don't know how to math tag sq. root or integral
    Since \tan(x)=\frac{\sin(x)}{\cos(x)}

    we see that

    \tan(x)\cdot\\sqrt{cos(x)}=\frac{\sin(x)}{\cos(x)}  \cdot\sqrt{\cos(x)}=\frac{\sin(x)}{\sqrt{\cos(x)}}

    So now realize taht -D_x\bigg[\cos(x)\bigg]=\sin(x)

    can you go from there?
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