Mathematical problems for self assessment

Sample Problems

APPLICATIONS OF INTEGRATION I

 

For Questions 1 and 2 you can assume the following formulae:

 

1. Find the area under the curve from x = 0 to x = 1 using the limit of a sum technique.

[Ans. ].

 

2. Find the area under the curve between x = 0 and x = 2 using the limit of a sum technique.

[Ans. 8].

 

3. Find the volume of the solid formed when the function between and is rotated about the x axis.

[Ans. ].

 

4. Find the volume of the solid formed when the cusp function is rotated about the y axis between and .

[Ans. ].

 

5. Find the co-ordinates of the centre of mass of the plane lamina given in the figure below:

[Ans. ].

 

6. Find the co-ordinates of the centre of mass of the plane lamina given in the figure below:

[Ans. ].

 

7. Find the co-ordinates of the centre of mass of the plane lamina given in the figure below:

[Ans. ].