Question:

Given: Problem statement: Using integration, find the area of the region bounded by circle $x^2 + y^2 = 16$ which is exterior to parabola $y^2 = 6x$.
Step 1: Find equations of lines / curves bounding region:
Derive line equations $y = m x + c$ for all side segments. [1.0 Mark]
Step 2: Determine intersection coordinates:
Solve boundary equations to obtain integration limits. [1.0 Mark]
Step 3: Set up area integrals over split sub-intervals:
Write $A = \int_{x_1}^{x_2} y_{top} dx + \int_{x_2}^{x_3} y_{top} dx - \int_{x_1}^{x_3} y_{bottom} dx$. [1.0 Mark]
Step 4: Execute definite integration:
Evaluate anti-derivatives for each segment. [1.0 Mark]
Step 5: Compute final total area:
Sum results to obtain total bounded area in square units. [1.0 Mark]
Conclusion: Total enclosed area calculated.

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🎯 Official CBSE Marking Scheme:
Finding boundary line equations: 1.0 Mark
Evaluating intersection points/limits: 1.0 Mark
Setting up split sub-interval integrals: 1.0 Mark
Evaluating definite integrals: 1.0 Mark
Evaluating final total bounded area: 1.0 Mark