Question 1121445
<font face="Times New Roman" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \int^{\small{\pi/2}}_{\small{0}}\,\cos(x)\ -\ \cos^2(x)\,dx]


Apply linearity:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \int^{\small{\pi/2}}_{\small{0}}\,\cos(x)\ -\ \int^{\small{\pi/2}}_{\small{0}}\,\cos^2(x)\,dx]



The first term is a standard integral, I'll leave that to you.  Use the reduction formula for the second term:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \int\,\cos^n(x)\,dx\ =\ \(\frac{n-1}{n}\,\int\,\cos^{n-2}(x)\,dx\)\ +\ \frac{\cos^{n-1}(x)\sin(x)}{n}]


And for this problem *[tex \Large n\ =\ 2], hence the antiderivative for the second term is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\cos(x)\sin(x)\ +\ x}{2}\ +\ C] 


You can do your own arithmetic
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
</font>