1322Midterm1AS14Solution - MAT1322-3X Solution to Midterm...

MAT1322\-3X Solution to Midterm 1(A) Summer 2014
1
Solution to Midterm Examination 1 (version A)
MAT 1322-3X, Summer 2014
1. (3 marks) Use the definition of improper integrals to find the value of improper integral
3
2
1
3 6
dx
x -
∫
.
Solution .
1 1
lim
3
2. (3 marks) Use the comparison test to show that improper integral
3
1
2 1
1
2
2 1 2
x x
x
x x
=
-
. Since
1 1
2 2
dx x dx
x
∞ ∞
-
=
∫ ∫
diverges, improper integral
.
3. (3 marks) Find the area of the region bounded by the graph of y = x
2
– 2 x + 1 and the graph
of y = -2 x
2
+ 4 x + 1.
2