Math Help - 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

2. Try $u=\cos(x)$

3. 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?