Definite Integral help please

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May 22nd 2008, 12:22 PM
bloomsgal8

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
May 22nd 2008, 12:24 PM
PaulRS

Try $u=\cos(x)$ (Wink)
May 22nd 2008, 12:28 PM
Mathstud28

Quote:

Originally Posted by bloomsgal8

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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