Integrals class 12 maths | chapter7 | ILATE rule | Ex-7.6 | скачать в хорошем качестве

Integrals class 12 maths | chapter7 | ILATE rule | Ex-7.6 |

#ILATERule #IntegrationTricks #Class12Maths #cbse2026 #ncertsolutions #ncertClass12 #ILATEMethod #Integrationshortcuts #MathsByRamSir #Boards2026 #ExamPreparation #MathsTricksHindi #NCERTExercise7_6 #JEEFoundation #StudyWithMeIndia #MathsMotivation #ConceptWithTrick #MathsDhakadTrick #IntegrationMadeEasy #ILATETrick #ILATERuleExplained #MathsShortcuts #NCERTMaths #Class12Boards #MathsLecture #MathsReels #YouTubeMaths #StudyHack #StudySmart #ExamTips #BoardExamPrep #MathsGuide #MathsWithTricks #MathsForEveryone #NCERTChapter7 #IntegrationMethod #LearnMaths #MathsMagic #MathsFormula #MathematicsLove #MathsCommunity #DailyMaths #MathsTeacherIndia s video, titled “ILATE Rule Masterclass – NCERT Ex 7.6 Full Solution | धाकड़ Technique 🔥” by DECODE MATHS BY RAM SIR, provides a comprehensive guide to solving integration problems using the ILATE rule (also known as Integration by Parts). The video covers the following key points: • Understanding the ILATE Rule (0:04-1:54): The instructor explains the acronym ILATE: • I: Inverse Trigonometric Function (e.g., sin⁻¹x, cos⁻¹x) • L: Logarithmic Function (e.g., log x) • A: Algebraic Expression (e.g., x, x²) • T: Trigonometric Function (e.g., sin x, cos x) • E: Exponential Function (e.g., eˣ, aˣ) This sequence determines the preference for selecting the first function in the integration by parts formula. • ILATE Rule Formula (1:59-4:21): The core formula for integration by parts is explained: ∫f₁(x)f₂(x) dx = f₁(x)∫f₂(x) dx - ∫[f₁'(x)∫f₂(x) dx] dx. The importance of remembering this formula for solving problems is emphasized. • Problem Solving with ILATE Rule (NCERT Exercise 7.6): • Example 1: x sin x (4:24-5:50): The first example demonstrates applying the ILATE rule step-by-step. • Trick for Algebraic First Function (5:53-8:56): A "dhakad technique" (powerful trick) is introduced for cases where the first function is an algebraic polynomial. This trick involves successive differentiation of the first function until it becomes zero and successive integration of the second function, followed by cross-multiplication with alternating signs. This significantly simplifie the process. • Example 2: x sin 3x (9:04-11:58): This example further illustrates the application of both the standard formula and the trick. • Example 3: x² eˣ (12:01-16:16): This problem demonstrates how to apply the ILATE rule multiple times when the first function's derivative does not immediately become zero, and also shows how the trick can be used to quickly verify the answer. • Example 4: x log x (16:31-18:00): This example highlights a scenario where the logarithmic function is prioritized as the first function according to ILATE. • Example 5: x² log x (18:29-19:36): Another example with a logarithmic function and an algebraic function. • Example 6: x sin⁻¹x (19:57-31:18): This complex example uses a substitution method (sin⁻¹x = θ) to transform the integral into a simpler form that can be solved with ILATE, requiring careful conversion back to the original variable. It also discusses how to integrate the resulting terms using standard formulas. • Example 7: x tan⁻¹x (31:47-33:59): Similar to the previous example, this problem demonstrates applying ILATE with an inverse trigonometric function. • Example 8: x cos⁻¹x (34:08-37:27): Another example involving an inverse trigonometric function, showing similar steps to x sin⁻¹x. • Example 9: (sin⁻¹x)² (37:37-41:12): This example involves substitution to simplify the integral before applying ILATE twice. • Example 10: x cos⁻¹x / √(1-x²) (41:17-45:34): This problem involves substitution and then applying ILATE. • Example 11: x sec²x (45:45-46:27): A straightforward application of ILATE with algebraic and trigonometric functions. • Special Type: eˣ (f(x) + f'(x)) (58:49-1:01:30): The instructor introduces a special integration form where the integral of eˣ(f(x) + f'(x)) dx equals eˣf(x) + C. Several examples are solved using this trick. • Integration of Exponential and Trigonometric Functions (1:07:05-1:15:58): The video tackles integrals of the form e^ax sin bx dx and e^ax cos bx dx, showing that these types of integrals require applying the ILATE rule twice. A shortcut formula is also provided for these specific cases. • Understanding Formulas (1:16:14-1:17:58): The instructor emphasizes the importance of memorizing key trigonometric formulas, especially those related to 2 tan⁻¹x, to simplify complex integrals.