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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 Integration Quiz-1

This is a free quiz/test based on the chapter Indefinite Integration from Class 12th Maths.This quiz covers only the basic concepts of the chapter. Give this quiz seriously and access you level of preparations.

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Class 12 NCERT Maths – Exercise 7.4 Solutions

Q1. Evaluate Solution:Let , so . Substitute: So, Final Answer: Q2. Evaluate Solution:Write , which matches the formula: Let , so . So, Substitute back : Final Answer: Q3. Evaluate Solution:Let . So, Substitute back : Final Answer: Q4. Evaluate Solution:Write , which matches the formula: Let . So, Substitute back : Final Answer: Q5.

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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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Complete Trigonometric Formulae (Class 11)

Trigonometry has a wide set of identities that simplify calculations and problem-solving. Here are the most important formulae, grouped by type, for your reference. 1. Trigonometric Functions of Sum and Difference of Two Angles 2. Product to Sum (or Product to Series) Formula 3. Sum to Product (or Series to Product) Formulas 4. Double Angle

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Class 12 NCERT Maths – Chapter 5 (Continuity and Differentiability) – Exercise 5.1 Solutions

Question 1. Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = -3, and at x = 5. Solution: To prove that a function is continuous at a point , we need to show: This requires that: 1. is defined,2. The left-hand limit (LHL) and right-hand limit

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🧮 Practice Sheet Level 2: Algebra (Based on Class 9 Concepts)

Solve the following questions. The questions are designed to test your conceptual understanding of algebra at a Class 9 level. This sheet includes evaluation, factorization, simplification, and solving equations. 📘 Section A: Evaluate the Expression Q1. Evaluate: Q2. Evaluate: Q3. Evaluate: Q4. Evaluate: Q5. Evaluate: Q6. Evaluate: Q7. Evaluate: Q8. Evaluate: Q9. Evaluate: Q10. Evaluate:

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🧮 Practice Sheet Level 1: Algebra (Based on Class 6 to 8 Concepts)

Solve the following questions. Show all necessary steps. Focus on evaluating, simplifying, and solving algebraic expressions and equations. 📘 Section A: Evaluate the Expression Q1. Evaluate: when Q2. Evaluate: when Q3. Evaluate: when Q4. Evaluate: when Q5. Evaluate: when Q6. Evaluate: when Q7. Evaluate: when Q8. Evaluate: when Q9. Evaluate: when Q10. Evaluate: when 📗

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Class 12 NCERT Maths – Chapter 4 (Determinants) – Exercise 4.3 Solutions

Question 1: Evaluate Minors and Cofactors of the elements of the following determinant: (i) Solution: Element a₁₁ = 2 Element a₁₂ = -4 Element a₂₁ = 0 Element a₂₂ = 3 Summary Table: (ii) Solution: Element a₁₁ = a Element a₁₂ = c Element a₂₁ = b Element a₂₂ = d Summary Table: Question 2:

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Author name: Ankur Negi