Evaluate the definite integral:

Question

Philoid · Accepted Answer

Let

Also, let sinx – cosx = t

Differentiating both sides, we get,

(cosx + sinx) dx = dt

When x = 0, t = -1

And when , t = 0

Now,

(sinx – cosx)² = t²

1 – 2 sinx.cosx = t²

Sin2x = 1 – t²

Putting all the values, we get the integral,