Question

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

Answer 1

Answer:

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 =$\frac{1}{2} \cdot \frac{3}{2} \cdot 3 =\frac{9}{4}$

Red triangle x=0 to 2.5

base = 5/2  and height = 5

Area of red part =$\frac{1}{2} \cdot \frac{5}{2} \cdot 5 =\frac{25}{4}$

Total area=$\frac{25}{4} +\frac{9}{4} =\frac{17}{2}$