Chapter 5.5, Problem 14ES

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) ${\displaystyle {\int }_0^2\left(1-\frac{1}{2}x\right)dx}$

(b) ${\displaystyle {\int }_{-1}^1\left(1-\frac{1}{2}x\right)dx}$

(c) ${\displaystyle {\int }_2^3\left(1-\frac{1}{2}x\right)dx}$

(d) ${\displaystyle {\int }_0^3\left(1-\frac{1}{2}x\right)dx}$