Mathematics for Biomedical Engineering
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. 
].
MJC