SOLUTION: Find the exact value of the integral cosx-cos^2(x) in terms of x from x=0 to x=pi/2
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Question 1121445: Find the exact value of the integral cosx-cos^2(x) in terms of x from x=0 to x=pi/2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ -\ \cos^2(x)\,dx)
Apply linearity:
\ -\ \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:
\,dx\ =\ \(\frac{n-1}{n}\,\int\,\cos^{n-2}(x)\,dx\)\ +\ \frac{\cos^{n-1}(x)\sin(x)}{n})
And for this problem 
, hence the antiderivative for the second term is:
\sin(x)\ +\ x}{2}\ +\ C)
You can do your own arithmetic
John
My calculator said it, I believe it, that settles it
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