Find the area of the region bounded by the curves y = sin(x), y = cos(x), x = 0, and x = 𝜋/2.

Answer 1

Another reasonable interpretation of the question is to assume it is asking for positive area, i.e. that the area should be positive regardless of which function is above, i.e. the integral of the absolute value of the difference of the 2 functions. Using that interpretation, we note that cosx lies above sinx, on [0 , π/4]. (And, since the above answer came out as 0, we can just double the area between the curves on [0 , π/4].)

Area = 2⋅∫₀^π/4 (cosx - sinx)dx = 2 (sinx + cosx)]₀^π/4 = 2√2 - 2

Answer 2