Question

\int_0^\frac \pi2$$\frac {\pi}{20} cos\ 2x\ dx

Answer 1

Let I = \int_0^\frac \pi2$$\frac {\pi}{20} cos\ 2x\ dx

∫cos 2x dx = $\frac {sin\ 2x}{2}$ = F(x)

By second fundamental theorem of calculus,we obtain:

I = F($\frac \pi2$) - F(0)

= $\frac 12$[sin2($\frac \pi2$) - sin 0]

= $\frac 12$[sin$\pi$ - sin0]

= $\frac 12$[0 - 0]
= 0