Q43 of 865 Page 19

Evaluate the following integrals:

Let

We have

We know cos2θ = 1 – 2sin²θ = 2cos²θ – 1

Hence, in the numerator, we can write

In the denominator, we can write

Therefore, we can write the integral as

[∵ sec²θ – tan²θ = 1]

Recall and

Thus,

Evaluate the following integrals:

If and, find f(x).