Question

Coordinate axes, the curve y = sin (x) and the straight line x = 3π/2 limit one area.

Determine the size of this area.

Answer 1

Solution. Sketch the desired area

Using the properties of the integral, the desired area is equal to

$$S=\int _0^\pi (sin x-0)dx+\int _\pi^{\frac {3\pi}{2}}(0-sinx)dx$$

$$S=\int _0^\pi sin xdx-\int _\pi^{\frac {3\pi}{2}}sinxdx$$

$$S=-cosx|_0^{\pi}+cosx|_{\pi}^{\frac {3\pi}{2}}=1+1+0+1=3$$

Answer. 3.