Question

1- Find the area enclosed by the given curves.

Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line   above left by y = x + 4, and above right by y = - x ² + 10.

2- Find the area enclosed by the given curves.

Find the area of the "triangular" region in the first quadrant that is bounded above by the curve  , below by the curve y = e ^x, and on the right by the line x = ln 4.

3- Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the .

y = x + 3, y = 0, x = -3, x = 5

4-Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the .

y =  , y = - x + 10

5- Find the volume of the solid generated by revolving the region about the y-axis.

The region in the first quadrant bounded on the left by the circle x ² + y ² = 1, on the right by the line  , and above by the line y = 1

6- Find the volume of the solid generated by revolving the region about the y-axis.

The region in the first quadrant bounded on the left by y =  , on the right by the line  , and above by the line y = 2

7- Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.

y = 5x, y = -  , x = 1

8-

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis.

x = 8y ², x = 8  

9-

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method.

The region bounded by y = 4 , y = 4, and x = 0 about the y-axis.

Answer 1