Chapter 7 Quiz

Calculators allowed

1. Find the area between the functions y=x2 and y=x3

a) 1/3 b) 1/12 c) 7/12 d) 1/4

2. Find the area between the y=cos(x) and y=sin(x) from -3∏/4 to 5∏/4

a) 0 b) 4/√2 c) 8/√2 d) 4

3. The base of a solid is the region bounded by y=x2 and the line y=1. Each cross section perpendicular to the x-axis is a rectangle whose height is twice as long as the length. If the shorter side is always the base, what is the volume of the solid?

a) 2/4 b) 4/5 c) 4/7 d) 3/2

4. The base of a solid is the region bounded by y=x3 and y=x. Each cross section perpendicular to the y-axis is a square. What is the volume of the solid?

a) .076 b) 1.202 c) .598 d) .202

5. Determine the volume of the solid obtained by rotating the area enclosed by y=ex and y=x+2 around the line y=-1

a) 29.346 b) 33.326 c) 21.093 d) 37.203

6. Determine the volume of the solid obtained by rotating the area enclosed by y=sin(x), x-axis, x=0, and x=∏ around the line y=1

a)3.394 b) 2.429 c) 1.235 d) 2.989

7. Determine the volume of the solid obtained by rotating the area enclosed by y= √x and y=x2 around the y-axis.

a).673 b) 1.340 c) .942 d) .471

8. Determine the volume of the solid obtained by rotating the area enclosed by y=x and y=0 from 0 to 2 around the y-axis

a) 13.923 b) 19.238 c) 11.239 d) 16.755

9. What is the length of the curve y=ex from 0 to 1?

a) 1.642 b) 1.120 c) 1.339 d) 2.000

10. What is the length of the curve y=sin(x) from 0 to ∏?

a) 2.828 b) 3.229 c) 3.142 d) 2.201

Answer key

• 1 b• 2 c• 3 b• 4 a• 5 a• 6 b• 7 c• 8 d• 9 a• 10 a