Chapter 4, Problem 19PS

(a)

To determine

To calculate: Both the upper and lower sums that approximate the area of the region bounded by the line $y=mx$ in the first quadrant and the line $x=b$ where the step-size $\Delta x=\frac{b}{4}$.

(b)

To determine

To calculate: Both the upper and lower sums that approximate the area of the region bounded by the line $y=mx$ in the first quadrant and the line $x=b$ where the step-size $\Delta x=\frac{b}{n}$.

(c)

To determine

To calculate: The area of the bounded region using the upper and lower sums obtained earlier by letting n tending towards infinity and to conclude that the area is the area of a triangle.