यदि [x] महत्तम पूर्णांक फलन (greatest integer function) को दर्शाता है जो x से छोटा या उसके बराबर है, तो समाकल (integral) ∫-π/2π/2 [[x] - sin(x)] dx का मान किसके 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 ?