Evaluate
OR

Evaluate .
[CBSE 2018]

Question

Evaluate 
OR

Evaluate .
[CBSE 2018]

Philoid · Accepted Answer

Let I = 
Here, we express the denominator in terms (sin x &ndash; cos x) which is the integration of numerator.

Clearly,

Therefore,  becomes,

Let, sin x &ndash; cos x = t.

Then, d(sin x &ndash; cos x) = dt

(cos x + sin x)dx = dt.
Now the limits of integration also change,
at x = 0t = sin0 &ndash; cos0 = &ndash; 1 and at x =

&there4;

OR

(let)

When ; a = 1, b = 3

By, the definition we know that,

As  &there4;