If f : R → R be a continuous function satisfying ∫0π/2 f(sin 2x) · sin x dx + α ∫0π/4 f(cos 2x) · cos x dx = 0, then the value of α is equal to:

The value of the definite integral I = ∫0π x dx1 + cos2x is:

Evaluate the definite integral: ∫01 2x + 5x2 + 3x + 2 dx

What is the area enclosed by the curve y = x2 and the x-axis from x = -2 to x = 2?