Properties of Definite Integrals

Description:In this post, we discuss some important properties of definite integrals which simplify calculations and make evaluation easier. These properties are frequently used in NCERT Class 12 Mathematics and are very useful for solving integration problems in board exams and competitive exams like JEE. Introduction The definite integral not only represents the area under a

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Class 12 NCERT Maths – Chapter 7, Exercise 7.6 Solutions (Integrals by parts)

Question 1: Integrate Solution: Take     Differentiate :  Integrate :  By parts formula: Substitute values: Final Answer: Question 2: Integrate Solution: Take     Differentiate :  Integrate :  By parts formula: Substitute values: Final Answer: Question 3: Integrate Solution: Take     Differentiate :  Integrate :  By parts formula: Substitute values: Now, solve using by parts again:

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Class 12 NCERT Maths – Chapter 7, Exercise 7.3 Solutions (Integrals of Trigonometric Functions)

Q1. Find Solution:Recall, So, Therefore, Integrate, Final Answer: Q2. Find Solution:Use product-to-sum: So, Integrate, Final Answer: Q3. Find Solution:First, use product-to-sum for two cosines: So, Now, Now expand both terms: So, Now integrate term by term: Final Answer: Q4. Find Solution:Recall, So, Integrate, Using, So, We can also simplify this further Using, So, Substitute this

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Partial Fractions and Formulae

What are Partial Fractions? Steps for Using Partial Fractions Types of Partial Fractions Notes Tip:Whenever you see a rational function, first try to write it in one of the forms above. This will make integration much easier! Example of Partial Fraction Decomposition Express as a sum of partial fractions. Step 1: Identify the Form: The

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