Sketch the region enclosed by the given curves. Decided whether to integrate with respect to x or y. Find the area of the region. y = sin(x), y = x, x = pi/2, x = pi
The graph was made with an online graphing calculator. It is attached below.
For the integration, I would integrate with respect to x, as:
`int_(pi/2)^pi(x - sin (x))dx`
`x^2/2` + cos(x), from pi/2 to pi
`(pi^2)/2` + (-1) - `(pi^2)/8` - 0
`(3pi^2)/8` - 1 = 2.7011 square units