Given that ∫-∞∞ e-x2 dx = √π. If a and b are positive integers, what is the value of the integral ∫-∞∞ e-a(x+b)2 dx?

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 ?