Calculus

Math 1 Crew Test 8

1. Find the area of the region bounded by

2. Use an integral with respect to y to find the area of the region bounded by

3. The base of a solid is the region bounded by the curves The cross sections of the solid perpendicular to the base and perpendicular to the x-axis are equilateral triangles. Find the volume of the solid.

4. Let R be the region bounded by the curves Use disks or washers to find the volume of the solid generated when R is revolved about the x-axis.

5. Let R be the region bounded by the curves Use disks or washers to find the volume of the solid generated when R is revolved about the y-axis.

6. Let R be the region in Quadrant 1 bounded by the curves Use cylindrical shells to find the volume of the solid generated when R is revolved about the y-axis.

7. Let R be the region bounded by the curves Use cylindrical shells to find the volume of the solid generated when R is revolved about the line y = 2.

8. Find the mass of the thin bar with density function

9. A water tank is shaped like an inverted cone with radius 4 m and height 6 m. If the tank is full, how much work is required to empty the tank by pumping the water to a level 2 m above the top of the tank.

10. A water tank is shaped like a sphere with a radius of 5 m. If the tank is half full, how much work is required to empty the tank by pumping the water to the top of the tank.

y = 5x − x2 and y = x2 − 3x.

x = 2y2 and y = 1 2 x − 2.

y = cos x and y = 0 for -π 2 ≤ x ≤π 2.

y = 1+ sin x and y = 0 for 0 ≤ x ≤ 3π 2.

y = 2 x and y = 2x2 .

y = x +1, y = 2x, and x = 0.

x = y2 and x = 1.

ρ x( )= x 17 − x2 for 1≤ x ≤ 4.