Question

Let S = (0, 2π) - {π/2, 3π/4, 3π/2, 7π/4 }. Let y = y(x), x ∈ S, be the solution curve of the differential equation dy/dx = 1/(1 + sin 2x), y(π/4) = 1/2. if the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve y = √2sin x is kπ/12, then k is equal to______.

Answer 1

= \(\frac{12\pi+7\pi + 23}{12}=\frac{42\pi}{12}\) 

= \(\frac{k\pi}{12}\) 

⇒ k = 42