Application Of Integrals

Step 1: Set up the equation.
The area of the region is bounded by the curve and the line . To find the limits of integration, we need to express in terms of from the equation : We are given the line , so we will integrate from to to find the area.

Step 2: Find the area using integration.
The area between the curve and the line is given by: Since the function is symmetric, we only need to integrate the positive half.

Step 3: Solve the integral.
To solve , we use the power rule: Thus, the area is:

Step 4: Conclusion.
The area of the region bounded by the curve and the line is square units.