Area Under Simple Curves

Step 1: Finding Points of Intersection The given curves are: To find the points of intersection, set both equations equal to each other: Solving for : Thus, the curves intersect at and .
Step 2: Setting up the Area Integral The area between the curves is given by: Simplifying the integrand:
Step 3: Evaluating the Integral First integral: Second integral: Using the standard formula: we get: Evaluating from to : Thus,
Step 4: Final Calculation Thus, the correct answer is option (3): .