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Mathematical problems for self assessment

Sample Problems
APPLICATIONS OF INTEGRATION I

 

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

formula1

 

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

[Ans. image placeholder].

 

2. Find the area under the curve image placeholder 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 image placeholder between image placeholder and image placeholder is rotated about the x axis.

[Ans. image placeholder].

 

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

[Ans. image placeholder].

 

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

fig1

[Ans. image placeholder].

 

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

fig2

[Ans. image placeholder].

 

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

fig3

[Ans. image placeholder].