Area Under Simple Curves

Step 1: Find the points of intersection:

1. Between and : Only is in the first quadrant.

2. Between and x-axis ( ):

3. Between and x-axis:

Step 2: Set up the integral for the area:

The region is bounded by: - From to : between and x-axis - From to : between and x-axis

Total area :

Step 3: Calculate total area:

Conclusion: The area of the region is .

We are asked to find the area between the line , , and the interval .
First, express in terms of : Now, the limits of integration are and .
The area is found by integrating the expression for : Evaluating the integral: Substitute the limits:
Thus, the area is .