Integration

1. Find .
2. (a) Find , where is a constant.
   (b) Find the value of for which .
3. Given that and that , find .
4. Find the equation of the curve with gradient function which passes through the point .
5. (a) Sketch the curve .
   (b) Find the area of the region enclosed by the curve and the -axis.
6. The diagram below shows the curve , where is a positive constant.
   

Find the area of the shaded region in terms of .

7. In this question you must show detailed reasoning.

The diagram shows part of the curve .

Find the area enclosed between the curve and the -axis. Give your answer in exact form.
8. In this question you must show detailed reasoning.

The diagram shows the curve .

The shaded region shown is bounded by the curve, the -axis and the line .
The shaded region has area 10 square units.
Find the value of . Give your answer to 3 significant figures.