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

Question

Question

Answer 1

संकल्पना:

निश्चित समाकल:

यदि ∫ f(x) dx = g(x) + C तो \(\rm \int_a^b f(x)\ dx = [ g(x)]_a^b\) = g(b) - g(a)

गणना:

माना कि 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