What is the total mass of a rod if its linear density is given by ρ(x) = sin x and it is oriented along the X-axis over the interval [π2, π]?

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

What is the value of the definite integral ∫0π/2 a cos x + b sin xsin x + cos x dx ?

The value of the integral ∫01 tan-1(x)1 + x2 dx is:

The value of the integral ∫0π/2 √(cos x)√(sin x) + √(cos x) dx is:

The value of the definite integral ∫-ππ cos2(x)1 + 3x dx is: