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(L-3) (Exercise 3.2A) 3.Indefinite Integration Class 12th Maths-2 #newindianera #conceptbatch

New Indian Era (NIE) - Prashant Tiwari・2 minutes read

The video covers various types of integration questions, focusing on the importance of substitution and providing formulas for solving different types of problems. It emphasizes the process of identifying troublesome elements, using appropriate substitutions, and simplifying the integration process to achieve the final answers.

Insights

  • Substitution is a key technique in integration, where one identifies troublesome elements and replaces them with suitable substitutions to simplify the problem.
  • The process of integration involves various types of questions, such as Type Two, which specifically focuses on substitution, emphasizing the significance of substituting the derivative of the denominator or troublesome elements to arrive at the solution.

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Recent questions

  • What is the importance of substitution in integration?

    Substitution simplifies complex integration problems by replacing troublesome elements with suitable substitutions.

  • How is the formula for substitution in integration derived?

    The formula involves adding x upon the derivative of the denominator in the numerator to facilitate the substitution process.

  • What is the process of substitution in integration?

    Substitution requires identifying the element causing difficulty and replacing it with a suitable substitution to ease the integration process.

  • When is double substitution required in integration problems?

    Double substitution is necessary for certain questions to simplify the integration process and arrive at the correct answer efficiently.

  • How is the integration of Cosec and Sec^2 solved using substitution?

    The integration of Cosec results in log mode t plus c, while Sec^2 is solved using the derivative of the denominator or the troublesome element in the substitution process.

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Summary

00:00

Mastering Integration Techniques Through Substitution

  • The video covers Exercise 3.2 A, focusing on Type One, Two, Three, and Four questions.
  • Type Two involves Substitution, emphasizing the importance of substitution in integration problem-solving.
  • The formula for substitution involves adding x upon the derivative of the denominator in the numerator.
  • The process of substitution requires identifying the element causing difficulty and replacing it with a suitable substitution.
  • The integration of t results in log mode denominator plus c, following the substitution formula.
  • Type Two questions involve substituting the derivative of the denominator or the troublesome element.
  • The integration of Cosec is log mode t plus c, with the substitution of x for t.
  • The derivative of Sec^2 is used to solve the integration problem.
  • Double substitution is required for certain questions, simplifying the process.
  • The integration of sin4x involves manipulating the terms to achieve the final answer.

30:30

Calculus: Integrals, Derivatives, and Solutions

  • The integral of π b squared is one.
  • When separating the whole square denominator, one will be left.
  • The integral of -2x / x s + 1 is dx1 + x s.
  • The integral of 1 / x sp 1dx minus the integral of 2x / x sk pw.
  • The derivative of x s - 1 is 2.
  • The integral of x s * x / x s * x x s can be taken out of the root.
  • The derivative of a square root of a + x k is x s * x.
  • The integral of x s in the root is a pure constant.
  • The integral of t x ba 2dx is log mod x.
  • The integral of a x + b c is solved by letting the numerator equal a in the denominator plus b derivative of the denominator.

01:03:10

Equations, Integration, and Logarithms: Mathematical Solutions

  • Numeration is equation number one, with its value placed in the numeration.
  • Derive the next page from equation number four, where equation number one becomes the integration of 2/13 * 2c x + 3sx 2c.
  • Simplify the bracket by separating Dino Minette, resulting in 2/1 p 3/1 * -2 sa x + 3c x upon 2c x + 3sx d.
  • The derivative of 2/13 x + 3/1 is 2/13, leading to the answer of log mode denominator + c log mode denominator p c.
  • Solve a question by equaling the integration in 20 p 12, determining the value of a as 5 and b as -1.
  • Integrate 5xx by putting one, simplifying the process by separating t why and integrating to get log mode denominator ps s.
  • Simplify the question by considering tan3x = tan2x + t x, leading to the final answer of log mod sec3x up 3 - log mod sec2x / 2 - log mod x + c.
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