Find the integral of (sin x - cos x) / (1 + sin x cos x) with limits 0 to π/2.

Solution:

If an integral has upper and lower limits, it is called a definite integral.

Let's see how we can find this integral.

Let I = \(\int_0^{\pi/2} \) (sin x - cos x) / (1 + sin x cos x) --- (1)

I = \(\int_0^{\pi/2} \) (sin (π/2 - x) - cos (π/2 - x))/(1 + sin (π/2 - x) cos (π/2 - x))

I= \(\int_0^{\pi/2} \) (cos x - sin x) / (1 + sin x cos x) --- (2)

Adding (1) and (2) together, we get

2I = 0

I = 0

Therefore, integral of (sin x - cos x) /(1 + sin x cos x) with limits 0 to π/2 is 0.

Find the integral of (sin x - cos x) / (1 + sin x cos x) with limits 0 to π/2.

Summary:

Answer: The integral of (sin x - cos x) / (1 + sin x cos x) with limits 0 to π/2 is 0.