Скачать или смотреть EXERCISE 3.6 (Definite Integrals) | INTEGRATION | Class 12 Math | FBISE | NBF

EXERCISE 3.6 (Definite Integrals) | INTEGRATION | Class 12 Math | Federal Board | National Book Foundation
In this lecture, we solve Exercise 3.6 (Definite Integrals) from Class 12 Mathematics – National Book Foundation (NBF), Federal Board (FBISE).
This chapter builds conceptual and practical understanding of definite integrals, region sketching, and area calculation using geometry.
The lecture explains each question step-by-step, including how to identify the bounded region, interpret integrals geometrically, and use standard area formulas (triangle, rectangle, trapezium, semicircle).
Students will learn how to evaluate definite integrals using limits, piecewise functions, and given diagrams.
This video is helpful for FSC Part-II students preparing for board exams and needing clarity in Integration & Definite Integral techniques.

TIMESTAMPS

00:00:00 – Q1(i) Sketch region & find area using geometry
00:06:26 – Q1(ii) Sketch region & find area using geometry
00:10:15 – Q1(iii) Sketch region & find area using geometry
00:15:41 – Q1(iv) Sketch region & find area using geometry
00:19:48 – Q1(v) Sketch region & find area using geometry
00:21:40 – Q1(vi) Sketch region & find area using geometry
00:22:31 – Q2(i) Evaluate definite integral for piecewise function
00:23:58 – Q2(ii) Evaluate definite integral for f(x)=piecewise
00:25:00 – Q2(iii) Evaluate definite integral for f(x)=piecewise
00:25:48 – Q2(iv) Evaluate definite integral for f(x)=piecewise
00:27:27 – Q3(i–vi) Evaluate integrals using given area diagram
00:30:22 – Q4 Solve definite integral
00:31:40 – Q5 Solve definite integral
00:32:58 – Q6 Solve definite integral
00:35:18 – Q7(i) Evaluate integrals using geometric formulas
00:40:03 – Q7(ii) Evaluate integrals using geometric formulas
00:45:00 – Q7(iii) Evaluate integrals using geometric formulas

📚 What You Will Learn

How to interpret definite integrals as area

Sketching the bounded region

Using geometric formulas to calculate area

Evaluating definite integrals of piecewise functions

Understanding area from graphs

Applying integration techniques for board exams

📝 Book Reference

National Book Foundation (NBF)
Class 12 – Mathematics (Federal Board)
Chapter: Integration – Definite Integrals (Exercise 3.6)

🔔 For Students

This lecture is designed for FSC Part-II, Federal Board, Punjab Boards, KPK, Sindh, Balochistan, and AJK students.
Complete board-style solutions included.

✅ Hashtags (15)

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✅ YouTube Tags

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