### Home > PC > Chapter 2 > Lesson 2.3.5 > Problem2-130

2-130.
1. Suppose we want to find the area under the curve f(x) over the interval 1 ≤ x ≤ 10 using 25 sub-intervals. What is the width of each rectangle? Homework Help ✎

1. What will the height of the first rectangle be if we use left-endpoint rectangles?

2. What will be the height of the first rectangle if we use right-endpoint rectangles?

3. What will be the height of the last rectangle if we use right-endpoint rectangles?

4. What will be the height of the last rectangle if we use left-endpoint rectangles?

5. How would your answers change if the interval were BxE and the width of each rectangle were W?

$\text{width }=\frac{\text{length of interval}}{\text{No. of rectangles}}$

$\text{width }=\frac{9}{25\text{ rectangles}}=.36$

x0 = 1 → height of rectangle = f(1)

Height of x1.

For right-endpoint, we start at x1 and go to the end. So you want the height at that xend.

For left-endpoint, we start at x0 and go to the xend-1. So you want the height − f(end − width).

x0 = B→height of rectangle = f(B)
x1 = B + width →height of rectangle = f(B + width)
xlast = E →height of rectangle = f(E)
xOneBeforeLast = E−width →height of rectangle = f(E − width)