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=

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )