The value of for which _0^ 2 ( x+t x) ,dx _0^ 2 ( x+t x)^2 ,dx is maximum lies in the…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The value of

t

for which

\frac{\int_0^{\frac{\pi}{2}}(\sin x+t\cos x)\,dx}{\sqrt{\int_0^{\frac{\pi}{2}}(\sin x+t\cos x)^2\,dx}}

is maximum lies in the interval: (a)

(0,\frac{1}{2})

(b)

(\frac{1}{2},\frac{3}{4})

(c)

(\frac{3}{4},\frac{5}{2})

(d)

(\frac{5}{2},\frac{3}{2})