Area Under Curves: One-Page Formula Sheet

Area Under Curves — formula sheet

Formulas

• A = ∫ₐᵇ |f(x)| dx
• Between curves: A = ∫ₐᵇ (f − g) dx where f ≥ g
• Area of ellipse = πab
• Area between y² = 4ax and x² = 4ay is 16a²/3

Key ideas

• Sketch the curves first
• Area is always positive: integrate |f|
• Between curves: ∫(upper − lower) dx
• Sometimes integrating in y is easier

Traps to avoid

• Not finding intersection points
• Negative area from below the x-axis
• Choosing the wrong upper curve

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