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

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steveschoen | College Teacher | (Level 1) Associate Educator

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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`

This gives:

`x^2/2` + cos(x), from pi/2 to pi

Giving:

`(pi^2)/2` + (-1) - `(pi^2)/8` - 0

Simplifying:

`(3pi^2)/8` - 1 = 2.7011 square units

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