Shortest way to solve Latest Definite Integration PYQs of JEE Mains| Part 1| Patterns Number 1,2 & 3

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This video introduces a "Short Trick Series" for solving definite integration problems, specifically focusing on JEE Mains exam patterns. The host, Ashish Sir, presents three integration shortcuts (0:00:03).

Here's a breakdown of the patterns and their applications:

Pattern 1: Kings Rule Short Form (0:01:38)
This is a widely known shortcut for definite integrals where ∫(a to b) f(x) dx can be simplified to (b - a) / 2 when f(x) converts to f(a + b - x) and the numerator and denominator cancel out after applying Kings Rule.

Pattern 2: Integration by Parts Shortcut (0:03:30)
This shortcut is useful when u is an algebraic function in ∫ u v dx. The formula is u v1 - u' v2 + u'' v3 - u''' v4 and so on, where u' denotes differentiation and v1, v2 denote consecutive integrations.
A special case for v = e^x is also discussed (0:05:19).

Pattern 3: Brand New Shortcut for Definite Integrals (0:06:44)
This pattern applies to definite integrals of the form ∫(-a to a) [Even Function] / [1 + b^(Odd Function)] dx.
The shortcut allows you to remove the -a limit and the 1 + b^(Odd Function) part, simplifying the integral to ∫(0 to a) [Even Function] dx (0:07:30).


The video emphasizes that this pattern can save significant steps in solving problems.
The video then demonstrates the application of Pattern 3 to several JEE Mains Previous Year Questions (PYQs):
JEE Mains PYQ 1 (2024): Solving for alpha using Pattern 3 (0:09:12).
JEE Mains PYQ 2 (2024): Applying Pattern 3 to a complex integral (0:11:13). The video notes this question also involves the "integration by parts shortcut" (Pattern 2) in a combined use (0:17:31).
JEE Mains PYQ 3 (2024): A combined use of Pattern 3 and Pattern 2 (0:17:31).
JEE Mains PYQ 4 (2022): Solving an integral involving a modulus function with Pattern 3 (0:21:01).
JEE Mains PYQ 5 (2022): Applying Pattern 3 to a complex trigonometric integral by transforming integration limits (0:22:45, 0:27:10).

The video concludes with a set of homework questions for viewers to practice these patterns (0:33:55).

Timestamps
00:00:00 Intro
00:00:03 Introduction to the Short Trick Series and the 3 Integration Shortcuts
00:01:38 Pattern 1: Quick Recap of the widely known Kings Rule Short Form
00:03:30 Pattern 2: Integration by Parts Shortcut
00:06:44 Pattern 3 Revealed: The New Shortcut for Definite Integrals
00:09:12 JEE Mains PYQ 1 (2024): Solving for alpha using Pattern 3
00:11:13 JEE Mains PYQ 2 (2024): Applying Pattern 3
00:17:31 JEE Mains PYQ 3 (2024): Combined use of Pattern 3 and the Integration by Parts Shortcut (Pattern 2)
00:21:01 JEE Mains PYQ 4 (2022): Solving an integral involving a modulus function with Pattern 3
00:22:45 JEE Mains PYQ: Transforming integration limits to fit the Pattern 3 structure
00:27:10 JEE Mains PYQ 5 (2022): Applying Pattern 3 to a complex trigonometric integral
00:33:55 Homework Questions and Final Thoughts



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