Chapter 5.5, Problem 16ES

Sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geometry, where needed.

(a) ${\displaystyle {\int }_{-10}^{-5}6dx}$

(b) ${\displaystyle {\int }_{-\pi /3}^{\pi /3}\sin xdx}$

(c) ${\displaystyle {\int }_0^3\left|x-2\right|dx}$

(d) ${\displaystyle {\int }_0^2\sqrt{4-x^2}dx}$