Chapter 5.5, Problem 13ES

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) ${\displaystyle {\int }_0^{3}xdx}$

(b) ${\displaystyle {\int }_{-2}^{-1}xdx}$

(c) ${\displaystyle {\int }_{-1}^{4}xdx}$

(d) ${\displaystyle {\int }_{-5}^{5}xdx}$