Mark H. answered • 12/08/19
Tutoring in Math and Science at all levels
The area between 2 curves is the integral of the difference in the functions, evaluated over the specified interval. You should sketch the functions to verify if the curves cross within the specified interval. If they do, you will need to integrate in pieces.
Also, you sometimes need to transform the equations to facilitate the integration.
In this case we have y = cos(x) and y = sin(x). Within the specified interval, these cross at x = pi/4. This means we will integrate from 0 to pi/4, and then double the value. (If you plot the curves, you can see the symmetry and the fact that that area from 0 to pi/4 is the same as the interval from pi/4 to pi/2.
In all cases, you take the absolute value of the definite integral.
I get 2*(√2 - 1) = ~ 0.818
