1322Midterm1BS14Solution - MAT1322-3X Solution to Midterm...

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