EXERCISE 3.8 (Definite Integrals) | INTEGRATION | Class 12 Math | FBISE | NBF

EXERCISE 3.8 (Definite Integrals) | INTEGRATION | Class 12 Math | Federal Board | National Book Foundation This lecture covers Exercise 3.8 of Class 12 Mathematics (Federal Board), focusing on Definite Integrals and their real-world applications. Each question is solved step by step using standard techniques of integration, area under curves, volume of solids of revolution, work done, and economic applications such as consumer and producer surplus. Perfect for FBISE students preparing for board exams. The lesson is based on National Book Foundation prescribed textbook and follows the official syllabus guidelines. Concepts are explained conceptually and mathematically to help you understand definite integrals deeply and apply them confidently in problem solving. --- Timestamps 00:00:00 - Q1 Area bounded by y = x square, x axis, x = 1 to 3 00:08:02 - Q2 Area under y = square root of (6x + 4), x = 0 to 2 00:15:38 - Q3 Area bounded by y square = 4x and x = 3 00:26:03 - Q4 Areas of region A and region B for y = 1 by 2 (0.2 x square + x) 00:40:10 - Q5 Area bounded by y = 1 + cos x and y = -1 + sin x 01:00:32 - Q6 Area bounded by y = x, y = -2x, and x = 3 01:09:48 - Q7 Area between y = x + 6 and y = x square, x = 0 to 2 01:17:50 - Q8 Area bounded by y = x cube + 1, x axis, and x = 1 01:25:34 - Q9 Area enclosed by x = y square and y = x - 2 01:36:22 - Q10 Volume when region under y = square root x (1 to 4) rotates about x axis 01:42:15 - Q11 Volumes: (i) y = square root (3 - x square) about x axis (ii) y = 3 - 2x about y axis 01:49:11 - Q12 (i) Distance travelled from S(t) in given interval 02:01:08 - Q12 (ii) Distance travelled in interval 02:10:20 - Q12 (iii) Distance travelled in interval 02:24:23 - Q13 Work done stretching spring 0.6 m with 50 N force 02:29:12 - Q14 Work done stretching 10 inch spring to 16 inch with force 3 by 2 x 02:37:08 - Q15 (i) Consumer and producer surplus (all three cases) 02:45:39- Q15 (ii) Consumer and producer surplus (all three cases) 02:57:53- Q15 (iii) Consumer and producer surplus (all three cases) 03:13:28 - Q16 Total revenue in 4 years for f(t) = 200 (t - 5) square. 03:17:28- Q17 Total revenue in 8 years for f(t) = 600 square root (1 + 3t). 03:22:18- Q18 Area bounded by f(x) = x cube - 2x square + 1, x = 1.5 in first quadrant. class 12 math, definite integrals, exercise 3.8, fbise math, federal board math, area under curve, volume of revolution, integration class 12, nbf math book, consumer surplus, producer surplus, work done by spring, solids of revolution, pakistan math board, calculus lecture, integration problems, board exam preparation, math solutions, class 12 calculus