The value of the integral ∫_0^π/2 3√(cosθ)(√(cosθ) + √(sinθ))^5dθ equals ______.

Correct option is A. 0.50
I=3∫_0^π/2√(cos θ)(√(sinθ)+√(cosθ))^5=3 ∫_0^π/23√(sinθ)dθ(√(cosθ)+√(sinθ))^5⇒∫_0^π/23√(cos θ)(√(sinθ)+√(cosθ))^5=3 ∫_0^π/2√(sinθ)dθ(√(cosθ)+√(sinθ))^5⇒ 2I=3∫_0^π/2dθ(√(sinθ)+√(cosθ))^42I3=∫_0^π/2^2 θ d θ(√(tanθ)+1)^4Let tanθ =t^2⇒I3=∫_0^infty[1(t+1)^3-1(t+1)^4]dtI=|-32(t+1)^2+1(t+1)^3|_0^∞=32-1=12