Question

Evaluate: \(\rm \int_{0}^{\pi/2}\cos 2x\ dx\)

Answer 1

Correct Answer - Option 1 : 0

Concept:

Definite Integral:

If ∫ f(x) dx = g(x) + C, then \(\rm \int_a^b f(x)\ dx = [ g(x)]_a^b\) = g(b) - g(a).

Calculation:

Let I = \(\rm \int_{0}^{\pi/2}\cos 2x\ dx\)

⇒ I = \(\rm \left[\frac{\sin 2x}{2}\right]_0^{\pi/2}\)

⇒ I = \(\rm \left[\frac{\sin \pi}{2}-\frac{\sin 0}{2}\right]\)

⇒ I = 0.