Q44 of 865 Page 19

Evaluate the following integrals:

Let

We have sec²θ – tan²θ = cosec²θ – cot²θ = 1

Recall and

We also have and

⇒ I = 3(–cos x) – 4(sin x) + 6(tan x) – 7(–cot x) + c

∴ I = –3cosx – 4sinx + 6tanx + 7cotx + c

Thus,

Evaluate the following integrals:

If and, find f(x).

If f’(x) = x + b, f(1) = 5, f(2) = 13, find f(x).