Evaluate the integral by interpreting it in terms of areas. in other words, draw a picture of the region the integral represents, and find the area using high school geometry.
(0 → 4) ∫|2x−5|dx

17/2

Step-by-step explanation:

The graph of the given absolute funciton |2xd-5| is attached below

Find the area of each triangle using the graph

Take the area from x=0 to 4

break the graph into two right angle triangle

Area of the triangle = 1/2 times base times height

Green triangle x=2.5 to 4

base = 3/2  and height = 3

Area of green part =

Red triangle x=0 to 2.5

base = 5/2  and height = 5

Area of red part =

Total area=

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3