यदि ∫01 1(5 + 2x - 2x2)(1 + e(2 - 4x)) dx = 1α loge(α + 1β), जहाँ α, β > 0 है, तो α4 - β4 का मान बराबर है:

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 ?