If 4 ∫01 cot-1(1 - 2x + 4x2) dx = a tan-1 2 + b ln 5, then the value of (a + b) is equal to:

The value of the definite integral π4 ∫ sec3(x) dx0 is equal to:

The area bounded by the curve y = cos(x) and the x-axis between x = 0 and x = 2π (in sq. units) is:

Let f(x) = sin x and g(x) - f(x) = f(4 - x). What is the value of ∫04 f(x)g(x) dx ?