Evaluate the following integral as a limit of sums: ∫ cos x dx, x ∈ [0, π/2]

Question

Evaluate the following integral as a limit of sums:

\(\int\limits_{0}^{π/2} \) cos x dx

Answer 1

To find:  \(\int\limits_{0}^{π/2} \) cos x dx

Formula used:

where,

Here, f(x) = cos x and a = 0

Now, by putting x = 0 in f(x) we get,

f(0) = cos 0

f(h)

= cos h

Similarly, f(2h)

= cos 2h

Here A = 0 and B = h

Therefore,

Hence, the value of

 \(\int\limits_{0}^{π/2} \) cos x dx = 1