### Home > PC > Chapter 2 > Lesson 2.3.6 > Problem2-143

2-143.

Suppose we want to find the area under the function $f\left(x\right) = 2^{x}$ on the interval $1 ≤ x ≤ 3$

1. Sketch a graph of the curve shading the area of the region you are to find.

2. If left-endpoint rectangles are used will the estimate be too low or too high. Justify your answer.

Too low, as rectangles will be under the curve.

3. If you used right-endpoint rectangles to estimate the area, will that estimate be too low or too high. Justify your answer.

Too high, as rectangles will be above the curve.

4. Use your program to find an estimate using $20$ left- and right-endpoint rectangles.

$\text{Left}=8.360$, $\text{Right}=8.960$