Central Concept: Area = Integral of (upper - lower) over the bounded region

Branch 1 - Types of Regions:

• Between curve and x-axis
• Between two curves
• Bounded by multiple curves/lines
• Regions defined by inequalities

Branch 2 - Methods:

• Vertical strips (dx)
• Horizontal strips (dy)
• Parametric integration
• Polar area formula
• Symmetry exploitation

Branch 3 - Key Skills:

• Finding intersection points
• Determining upper/lower curves
• Splitting at crossing points
• Handling absolute values

Branch 4 - Standard Results:

• Parabola formulas (8$a^2$/3, 8a^$\frac{2}{3m^3}$, 16ab/3)
• Ellipse (piab)
• Quadratic between roots (|a|(beta-alpha)^3/6)
• Diamond (2ab)

Branch 5 - Common Traps:

• Signed vs geometric area
• Missing intersection points
• Wrong curve on top
• Not splitting at crossings

Branch 6 - JEE Patterns:

• Parabola + line (most common)
• Circle + line/parabola
• Absolute value regions
• Parameter-finding problems

Branch 7 - Advanced:

• Inverse function area
• Area bounds and estimation
• Optimization of bounded area
• Polar curves (cardioid, rose)