Evaluate the following definite integral: ∫cos^4x dx, x ∈ [0, π/2]

Question

Evaluate the following definite integral: 

\(\int\limits_0^{\pi/2} \)cos⁴x dx

Answer 1

 \(\int\limits_0^{\pi/2} \)cos⁴x dx =  \(\int\limits_0^{\pi/2} \)cos²x \(\times\)cos²xdx

(\(\because\) 1 + cos 2θ = 2 cos²θ)