Integration And Area Calculation

Step 1: Rewrite the equations. This is a circle with centre and radius .

Step 2: Points of intersection. Substitute in circle equation: On -axis, \Rightarrow . For , . So, points of intersection: and .

Step 3: Required area. We want area bounded by parabola, circle, and -axis above. In terms of : Thus, area is:

Step 4: Solve integration. First part: Second part: This represents a quarter circle of radius , so area = . Total Area:

Final Answer: