Name: _______________________________
Quiz 2 – Keys
1.
The shaded region as shown is enclosed by 3
functions:
2
0.5
15
7.5
0.1
y
x
y
x
y
x
=
−
+
=
+
=
Find its area.
This is a region where the boundary changes. And
the change takes place at
x = 5
.
Taking a vertical element as shown and the area
intergral is:
5
10
2
2
5
5
(
7.5)
0.1
( 0.5
15)
0.1
x
x
dx
x
x
dx
−
+
−
+
−
+
−
∫
∫
Carrying out the above integration and the area is 93.75 square units
0.5
15
y
x
=
−
+
7.5
y
x
=
+
2
0.1
y
x
=