MathematicsMedium38×since 2002Q3539Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 tanx(cosx−y)\tan x(\cos x - y)tanx(cosx−y). If the curve passes through the point (π4,0)\left( {{\pi \over 4},0} \right)(4π,0), then the value of ∫0π/2y dx\int\limits_0^{\pi /2} {y\,dx}0∫π/2ydx is equal to :A(2−2)+π2(2 - \sqrt 2 ) + {\pi \over {\sqrt 2 }}(2−2)+2πB2−π22 - {\pi \over {\sqrt 2 }}2−2πC(2+2)+π2(2 + \sqrt 2 ) + {\pi \over {\sqrt 2 }}(2+2)+2πD2+π22 + {\pi \over {\sqrt 2 }}2+2πCheck answerSkip