Application of Integrals

Board: CBSE Class: 12

Chapter Overview

The area bounded by y = f(x), x-axis, x=a, x=b is int_a^b f(x) dx. Area between two curves f(x) and g(x) is int_a^b |f(x) - g(x)| dx. The chapter covers area under curves, area between curves, and introduces volume of solids of revolution (disc and washer methods).

Topics Covered

Area Under a Curve
Area Between Curves
Area Bounded by Curves and Lines
Volume of Solids of Revolution
Disc Method
Washer Method

Key Formulas

Area = int_a^b f(x) dx

Between curves = int_a^b |f(x) - g(x)| dx

Volume = pi int_a^b [f(x)]^2 dx

Real-World Applications

Applications: Civil engineering (area/volume), physics (work, fluid pressure), architecture.

Study Tips

Tip: Sketch the curves first

Tip: Identify limits of integration carefully

Tip: Pay attention to which function is on top