Chapter 25.4, Problem 39E

To determine

To show: That ${\displaystyle \underset{0}{\overset{1}{\int }}xdx}>{\displaystyle \underset{0}{\overset{1}{\int }}{x}^{2}dx}$ and ${\displaystyle \underset{1}{\overset{2}{\int }}xdx}<{\displaystyle \underset{1}{\overset{2}{\int }}{x}^{2}dx}$ and explain the result in terms of area.