Evaluate the following integrals as a limit of sums:

Formula used:

where,

Let,

Here, f(x) = cos x

Now, by putting x = a in f(x) we get,

f(a) = cos a

f(a + h)

= cos (a + h)

Similarly, f(a + 2h)

= cos (a + 2h)

We know,

Therefore,

{∵ nh = b – a}

{∵ 2 cos A sin B = sin(A + B) – sin(A – B)}