Factorial Final Surge | JEE 2026 | JEE Mains 2026 + JEE ADV. 2026
Curated by: Factorial Academy (60 videos)
Complete Estimation in Definite Integration 🔥 | Concepts + Problems + JEE Advanced PYQs | Factorial Final Surge In this video we completely master the concept of ESTIMATION in DEFINITE INTEGRATION. This is one of the most powerful tools for solving difficult JEE Main and JEE Advanced problems where exact evaluation is not required and comparison techniques are used instead. In this session we discuss all major approaches used in estimation problems: 1. Area comparison using rectangles 2. Area comparison using trapezium and concavity 3. Series based estimation 4. Expansion based estimation The session includes several beautiful problems including JEE Advanced PYQs and conceptually rich problems that help build strong intuition. This video is part of the series FACTORIAL FINAL SURGE A must watch for serious JEE 2026 aspirants. --- Questions discussed in the video: 1. Let Sn = sum from k = 1 to n of n divided by (n² + kn + k²) and Tn = sum from k = 0 to n minus 1 of n divided by (n² + kn + k²) Then compare Sn and Tn with π divided by (3√3). --- 2. Which of the following inequalities are TRUE? (A) integral from 0 to 1 of x cos x dx is greater than or equal to 3 divided by 8 (B) integral from 0 to 1 of x sin x dx is greater than or equal to 3 divided by 10 (C) integral from 0 to 1 of x² cos x dx is greater than or equal to 1 divided by 2 (D) integral from 0 to 1 of x² sin x dx is greater than or equal to 2 divided by 9 JEE Advanced 2020 --- 3. Let S be the area of the region enclosed by y = e power minus x² y = 0 x = 0 x = 1 Then determine which statements are correct. --- 4. If I = sum from k = 1 to 98 of integral from k to k + 1 of (k + 1) divided by x(x + 1) dx Then determine the correct inequalities involving I. JEE Advanced PYQ --- 5. Prove that one by two is less than the integral from 0 to 1 of dx divided by square root of (4 minus x² plus x⁵) and that integral is less than pi by six. --- 6. Evaluate greatest integer of 1 + 1 divided by root 3 + 1 divided by root 5 + ... + 1 divided by root 121 --- 7. Evaluate greatest integer of the integral from 0 to 1 of 2 power x² dx --- 8. Prove that pi divided by 128 is less than the integral from pi by 4 to pi by 2 of (sin x) power 10 dx and that integral is less than pi by 4. --- 9. Prove that (e minus 1) divided by 3 is less than the integral from 1 to e of dx divided by (2 + ln x) and that integral is less than (e minus 1) divided by 2. --- If you want to master difficult JEE Mathematics problems and build deep conceptual clarity, subscribe to the channel. Telegram for updates and problems https://t.me/academyfactorial #JEEAdvanced #DefiniteIntegration #IntegrationTricks #FactorialFinalSurge #JEEMaths #JEE2026 #JEEMains2026 #JEEMaths2026