Sample Midterm
Problem 1. Compute
lim
nโโ
โ
X
i=1 ๎1 + 4i
n๎3๎2
n๎
Solution: 78
Problem 2. Evaluate the integral
Zx2โ1
โ2xโ1dx
Solution: 1
15โ2xโ1(3x2+ 2xโ13) + C
Problem 3. Evaluate the integral
Z3
0|x3โx2|dx
Sketch the region.
Solution: 137
12
Problem 4. Find the volume of the solid obtained by rotating the region
bounded by the curves y=x2and y= 4xโx2about y= 6, using the Method
of the disks. Sketch the region
Solution: 64ฯ
3.
Problem 5. Find the volume of the solid obtained by rotating the region
bounded by the curves y=x2and x=y2about x=โ1. Sketch the region
Solution: 29ฯ
30 .
1