Question

Evaluate : ∫₀^(π/2) sin 2x tan⁻¹(sin x) dx

Given d/dx F(x) = 1/√(2x – x²) and F(1) = 0, find F(x).

Evaluate : ∫₀^π e^(cos x)/(e^(cos x) + e^(−cos x)) dx

If ∫₋₂³ x² dx = k∫₀² x² dx + ∫₂³ x² dx, then the value of k is :