# Find area of regions bounded by curve and line

1. Dec 26, 2011

### sharks

The problem statement, all variables and given/known data
Find area of regions bounded by
x^2 + y^2 = 9, y = 2x, x-axis in the first quadrant

The attempt at a solution
So, i drew the graph of y against x in my copybook, and circle with origin (0,0), radius = 3 units. The line y = 2x cuts through the circle.
Transforming to polar coordinates, the new limits are:
0≤θ≤tan^-1(3) and 0≤r≤3
$$\int\int rdrd\theta$$
After integration, i get the final answer: (9/2)tan^-1(3)
However, the answer in my notes is: (9/2)tan^-1(2). Did i copy the wrong answer or is my work wrong? I'm not sure.

2. Dec 26, 2011

### SammyS

Staff Emeritus
...the new limits are:
0≤θ≤tan^-1(3)...​

3. Dec 26, 2011

### sharks

OK, so here is the graph: