find the area of one of the regions bounded by the curves y=sin x and y=cos x
You have to give a domain for this question, since there are an infinite number of regions bounded by the two curves.
I will find the first such region to the right of the origin.
First we need their intersection, ....
sinx = cosx
x = π/4 and x = 5π/4 (45° and 225°)
area = [integral] (sinx - cosx) dx from π/4 to 5π/4
= (-cosx - sinx) form π/4 to 5π/4
= -cos5/4 - sin5π/4 - (-cosπ/4 - sinπ/4)
= -(-1/√2) - (-1/√2) + 1/√2 + 1/√2
= 4/√2 or after rationalizing 2√2