Q. 39 - Calculus | StudyQuestionHub

StudyQuestionHub

Q. 39

Question

For each pair of functions f and g and each interval [a, b] in Exercises 38–40, use at least eight rectangles to approximate the area of the region between the graphs of f and g on the interval [a, b]. Your work should include graphs of f and g together with the rectangles that you used.

$f (x) = x, g (x) = 2, [- 4, 4]$

Step-by-Step Solution

Verified

Answer

$\int_{- 4}^{4} | x - 2 | d x = 20$

1Step 1. Given information

$f (x) = x, g (x) = 2, [- 4, 4]$

2Step 2. Calculating the area

$The area between curves is the area between a curve f (x) and a curve g (x) on an interval [a, b] given by,$

$A = \int_{a}^{b} | f (x) - g (x) | d x$

To calculate area,

$\int_{- 4}^{4} | x - 2 | d x = 20$

Other exercises in this chapter

For each function ff and interval [a,b] in Exercises 26–37, use definite integrals and the Fundamental Theorem of Calculus to find the exact values o

For each pair of functions f and g and each interval [a, b] in Exercises 38–40, use at least eight rectangles to approximate the area of the region betwee

For each pair of functions f and g and each interval [a, b] in Exercises 38–40, use at least eight rectangles to approximate the area of the region betwee

For each pair of functions f and g and interval [a,b] in Exercises 41–52, use definite integrals and the Fundamental Theorem of Calculus to find