Question

Evaluate the definite integral: $∫_0^\frac{π}{2}cos2xdx$

Answer 1

Let I=$∫_0^\frac{π}{2}cos2xdx$

$∫cos2xdx=(\frac{sin2x}{2})=F(x)$

By second fundamental theorem of calculus,we obtain

$I=F\frac{π}{2}-F(0)$

$=\frac{1}{2}[sin2(\frac{π}{2})-sin0]$

$=\frac{1}{2}[sinπ-sin0]$

$=\frac{1}{2}[0-0]=0$