\int ↙\stackrel{\frac{\pi}{0}{2}} {\sin x

CBSE Class 12 Math 2024 All Sets Solved Paper

Question : 6 of 20

Marks: +1, -0

∫ ↙{0}↖{\;{π}/{2}} \;{\sin x - \cos x}{1 + \sin x \cos x}/{dx}

is equal to

Solution:

Let

I = ∫↙{0}↖{\;}{π}/{2}\frac{\sin x - \cos x} {1 + \sin x \cos x} \;\; ....(1)

I = ∫↙{0}↖{\;}{π}/{2}\frac{\sin(\;{π}/{2} -x)-\cos (\;{π}/{2}-x)} {1 + \sin (\;{π}/{2} - x) \cos(\;{π}/{2} - x)}

I = ∫↙{0}↖{\;}{π}/{2}\frac{\cos x - \sin x} {1 + \sin x \cos x } \;\; ....(2)

Adding (1) and (2) together, we get
2I = 0
I = 0

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