A graphing calculator shows f(x) = sin x − cos x and g(x) = cos x − sin x intersecting directly
on the x axis at x = π/4, x = 9π/4 and exactly halfway between π/4 and 9π/4 at x = 5π/4.
The two curves have enclosed 2 identical elongated "bubbles" (symmetric to the x axis)
while tracing their courses.
One then sees by inspection that the absolute value of the area sought can be
represented by "2 times the integral [from π/4 to 5π/4] of {f(x) − g(x)} with
respect to x or 2∫[from π/4 to 5π/4]{f(x) − g(x)}dx or Choice C.
This integral is expressed as 2∫[from π/4 to 5π/4](2sin x − 2cos x)dx or
-4{cos x + sin x|[from π/4 to 5π/4]} which goes to 5.656854249 − -5.656854249
or 11.3137085 square units in agreement with Choice C.
