You are given the table below.
x 4 8 12 16 20
f(x) 11 25 16 9 31
use the table and n = 4 to estimate the following. because the data is not monotone (only increasing or only decreasing), you should sketch a possible graph and draw the rectangles.
20
(integral) f(x)dx
4

The integral value of is

Further explanation:

The equation of the line can be expressed as follows,

Given:

The value of the function at different values of can be written as follows,

Explanation:

The function is an increasing function if , than and the function is decreasing if

The can be obtained as follows,

The equation of line between the points can be obtained as follows,

Similarly the equation between the points can be expressed as follows,

The equation between the points can be expressed as follows,

The equation between the points can be expressed as follows,

The area under the line can be obtained as follows,

Similarly the area under the line can be obtained as follows,

The area under the line can be obtained as follows,

The area under the line can be obtained as follows,

Total area can be obtained as follows,

The integral value of is

Learn more:

1. Learn more about inverse of the functionhttps://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: College

Subject: Mathematics

Chapter: Integrals

Keywords: function, decreasing, increasing, monotonic, integral, monotone, data is not monotone, table, sketch, possible, graph, integration, area under the curve.