Application of Integrals – Class 12 Maths Chapter 8 | Area Under Curves & Between Curves
Here’s the complete guide for Chapter 8: Application of Integrals — Class 12 CBSE Maths: 🧠A. Key Concepts Area Under a Curve Area = ∫ a b f ( x ) d x \text{Area} = \int_a^b f(x)\,dx Valid when f ( x ) ≥ 0 f(x) \ge 0 on [ a , b ] [a,b] . Area Between Two Curves If f ( x ) ≥ g ( x ) f(x) \ge g(x) , then Area = ∫ a b [ f ( x ) − g ( x ) ] d x \text{Area} = \int_a^b [f(x) - g(x)]\,dx Area with Respect to Y-axis Area = ∫ c d [ x right ( y ) − x left ( y ) ] d y \text{Area} = \int_c^d [x_{\text{right}}(y) - x_{\text{left}}(y)]\,dy Combined Regions Split the integration region when functions intersect; sum individual definite integrals. 📘 B. NCERT Exercises & Solutions ✅ Ex 8.1 – Area under curve Identity: ∫ x 2 , ∫ x \int x^2, \int \sqrt{x} , etc. Check correct application of limits. ✅ Ex 8.2 – Area between curves Determine intersection points Use ∫ ( f − g ) d x \int (f - g) \,dx with proper limits ✅ Ex 8.3 – Area w.r...