Millersville University Name Answer Key
Department of Mathematics
MATH 211, Homework 02
January 30, 2006
Page 409, Exercise 18
Sketch and find the are of the region determined by the intersection of the curves:
y=x3
โ2x2, y =x2.
0.5 1 1.5 2 2.5 3 x
2
4
6
8
y
0.5 1 1.5 2 2.5 3 x
2
4
6
8
y
The curves intersect when the following equation is satisfied:
x3
โ2x2=x2
x3
โ3x2= 0
x2(xโ3) =
x= 0 or x= 3
Thus the area between the curves is
A=Z3
0
x2
โ๎x3
โ2x2๎dx
=Z3
0
โx3+ 3x2dx
=โ
1
4x4+x3๎
๎
๎
๎
3
0
=27
4
