Chapter 3 · Class 11-12 & JEE Main/Adv
Area Under Curves
21 topics in 8 parts
Area Under a Curve Area Between Curve and x-axis Area Between Two Curves Area Using Horizontal Strips Area Under a Parametric Curve Area in Polar Coordinates
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 21 topics in Area Under Curves
Different Cases of Bounded Area
- Area Bounded by Inverse of Function
- Determination of Function
- Determination of Parameters
- Shifting of Origin
- Regions Defined by Inequalities
Finding Area of Given Curve within Specified Limits
- Area Bounded by Curve & Axis
- Area of Conic Sections
Finding Function from Area Expression
- Finding Function from Area Expression
Finding Area Between Two or More Given Curves
- Area Between Two Curves
- Area Between Parabolas
- Area Between Circles & Lines
- Area Between Multiple Curves
- Equal Area Division by Line or Curve
Curve Tracing
- Curve Tracing
Mean Value Theorem of Integration
- Mean Value Theorem of Integration
Estimation of Area: Inequality Based
- Estimation of Area: Inequality Based
Area Involving Special & Piecewise Functions
- Greatest Integer & Fractional Part Functions
- Absolute Value Functions
- Max & Min Functions
- Signum & Piecewise Defined Functions
- Exponential Functions