Class 12 NCERT • Mathematics Part 2 (New Syllabus)
Mathematics Part 2 Ch 08: Application of Integrals
Select a topic or study module below to explore area under simple curves, area bounded by lines and curves, area between two curves, standard curve sketching (circles, parabolas, ellipses), and comprehensive textbook problem solutions.
Topic 01 • Area Under Simple Curves
Exploring Definite Integrals for Area Calculation, Curves y = f(x), X-axis bounds, and Elementary Geometric Regions
Topic 02 • Area Bounded by Y-axis Curves
Analyzing Horizontal Strip Integration x = g(y), Y-axis bounds, and Symmetry Considerations in Bounded Regions
Topic 03 • Standard Curves Area
Studying Standard Equations x2 + y2 = a2, y2 = 4ax, , and Quadrant Integration Tricks
Topic 04 • Area Between Two Curves
Investigating Intersection Points of Curves, Upper vs Lower Function Boundaries, and Split Integral Regions
Topic 05 • Lines with Circles & Parabolas
Examining Combined Regions Formed by Lines intersecting Circles, Parabolas, and Ellipses with Definite Integrals
Topic 06 • Region Partitioning
Analyzing Multi-Boundary Problems, Breaking Integrals at Intersection Ordinates, and Complex Sketching Techniques
Topic 07 • Geometry Applications
Studying Triangles Formed by Three Lines, Polygon Areas Using Integration, and Applied Optimization Problems
Module 08 • Solutions & Chapter Review