# 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. ].