Top Videos on Application of Integrals for Class 12 Core Maths by PW

Application of Integrals can become difficult when you have to translate a graph into a mathematical expression and determine the correct limits for calculating an area. A question may involve a parabola, two intersecting curves, or a region bounded by the coordinate axes. Commerce-based problems add another layer by applying integration to concepts such as cost, revenue, and consumer surplus.

The following PW videos cover these applications through worked examples, NCERT-based questions, and chapter revision. You can use them to understand graph-based problems, practise commerce applications, and strengthen your preparation for Class 12 board examinations.

Video 1: Revise Application of Integrals with Concepts and Board Questions

This one-shot lesson on PW Class 12 Commerce Wallah brings together important concepts from definite and indefinite integrals, including definite integrals as areas, evaluation methods, and substitution. It then covers areas under curves, parabolas, bounded regions, axis crossings, and modulus-based functions.

The session also includes commerce applications such as consumer and producer surplus, along with numerical problems based on demand and supply functions.

Worked examples, shortcuts, and previous-year questions make this video useful for revising the chapter in one sitting. Watch it when you need to connect geometrical and commerce-based applications or review key methods before a board test.

Practise the examples on paper alongside the lesson so that you can apply the methods independently.

Video 2: Understand Graphs and Solve NCERT-Based Application of Integrals Questions

When calculating the area under a curve, identifying the correct region and limits is essential. This NCERT-based lesson revises the coordinate geometry needed for Application of Integrals, including lines, parabolas, circles, ellipses and trigonometric graphs.

It explains area calculations using limits and covers solved questions involving bounded regions, latus rectum, coordinate axes, areas between curves, modulus functions, and first-quadrant regions.

The session also includes NCERT-style questions, previous-year questions, MCQs and approaches for solving problems efficiently. Use this video while working through NCERT exercises or preparing with sample papers.

Pay attention to how the graph determines the integration limits, then solve similar questions independently to improve your accuracy when dealing with unfamiliar regions.

Video 3: Practise Commerce Applications of Integrals for Class 12 Applied Maths

Application of Integrals also has practical uses in commerce-related mathematics. This full-chapter revision lesson covers definite integrals, limits, constants, substitution, integration by parts, and changing limits.

It applies these methods to total cost and revenue, marginal cost, consumer and producer surplus, equilibrium price and quantity, and linear commerce problems.

The lesson also revises lines, parabolas, areas bounded by coordinate axes and quadrant-based regions. Assertion-reasoning questions provide additional practice alongside numerical and graph-based problems

 If you are preparing for Class 12 Applied Mathematics, use this video to connect integration methods with commerce applications and revise important steps before your examination. Work through the calculations yourself to check whether you can apply each method without relying on the demonstrated solution.

How These Videos Help in Application of Integrals Preparation

These three PW videos cover different aspects of Application of Integrals, from full-chapter revision to graph-based questions and commerce applications. Use them according to your preparation needs.

• Revise the main concepts: Begin with the one-shot lesson to review integration methods, areas under curves, and important applications.

• Strengthen graph interpretation: Use the NCERT-based lesson to practise identifying bounded regions and selecting the correct limits for integration.

• Connect integration with commerce: Revise cost, revenue, marginal cost, consumer surplus and producer surplus through the Applied Mathematics lesson.

• Practise board-style questions: Attempt NCERT exercises, Class 12 previous-year questions and MCQs after watching the relevant sections.

• Improve accuracy through written practice: Draw the required graphs, write the limits carefully and complete calculations independently before checking the solutions.

Regular practice alongside these videos can help you identify the right method for different question types and revise the chapter more effectively before your Class 12 examination.

PW’s Application of Integrals videos help you revise integration concepts, understand areas under curves, and practise NCERT-based and commerce-related questions. 

Start with the full-chapter revision, strengthen your understanding of graphs and limits, and then practise applied problems. Combining video lessons with written question practice can help you improve accuracy and prepare more confidently for your Class 12 board exams.