Answer
a)$\Sigma^n_{i=1} \Delta x_i . \Delta m_i$ which is equal to L
b)$\Sigma^{n}_{i=1} \Delta x_i .\Delta M_i $which is equal to U
c) this area is U-L.
Work Step by Step
(a) The area of the shaded region is $\Sigma^n_{i=1} \Delta x_i . \Delta m_i$ which is equal to L
(b) The area of the shaded region is $\Sigma^{n}_{i=1} \Delta x_i .\Delta M_i $which is equal to U
(c) The area of the shaded region is the difference in the areas of the shaded regions shown in the second part
of the figure and the first part of the figure. Thus this area is U-L.
