Class 12 RS Aggarwal Chapter-14 Some Special Integrals Solutions - Free PDF Download
FAQs on Study Better With RS Aggarwal Class 12 Solutions Chapter-14 Some Special Integrals
1. What are the key types of special integrals covered in RS Aggarwal Class 12 Chapter 14?
RS Aggarwal Class 12 Chapter 14 focuses on a specific set of integral forms that frequently appear in exams. The solutions in this chapter primarily help you master integrals of the following types:
Integrals of the form ∫ dx / (ax² + bx + c), ∫ dx / √(ax² + bx + c), and ∫ (px + q) / (ax² + bx + c) dx.
Integrals involving square roots in the numerator, such as ∫ √(ax² + bx + c) dx.
These are solved by reducing the denominator or the expression inside the square root to the sum or difference of two squares.
2. How do you solve integrals of the form ∫ dx / (ax² + bx + c) using the method in RS Aggarwal solutions?
The step-by-step method provided in the RS Aggarwal solutions for this type of integral involves a key technique:
First, make the coefficient of x² equal to 1 by taking the coefficient 'a' common from the denominator.
Next, use the 'completing the square' method to express the quadratic expression in the form of (x + k)² ± m².
Finally, apply one of the standard integral formulas, such as ∫ dx / (x² + a²), ∫ dx / (x² - a²), or ∫ dx / (a² - x²), to get the final answer.
3. What is the correct approach for solving integrals like ∫ (px + q) / (ax² + bx + c) dx as per RS Aggarwal?
For integrals where the numerator is a linear expression (px + q), the correct method is to express the numerator in a specific form. The steps are:
Write the numerator as px + q = A * d/dx(ax² + bx + c) + B.
Find the values of the constants A and B by equating the coefficients of 'x' and the constant terms on both sides.
Split the original integral into two separate integrals: A ∫ [d/dx(denominator) / denominator] dx + B ∫ dx / (ax² + bx + c). The first part can be solved using substitution, and the second part is solved using the completing the square method.
4. Why is 'completing the square' such a critical technique in this chapter on Some Special Integrals?
Completing the square is a fundamental technique because it transforms a complex-looking quadratic expression, ax² + bx + c, into a simpler, recognisable format. This transformation is essential because it converts the integrand into one of the nine standard special integral forms. Without this step, you cannot directly apply the formulas for ∫ dx / (x² ± a²) or ∫ dx / √(x² ± a²), making the problem unsolvable by standard methods taught in this chapter.
5. How do you decide which specific integral formula to apply after completing the square?
The choice of formula depends entirely on the structure of the expression after you complete the square. You should check two things:
Is there a square root? If yes, you will use one of the inverse trigonometric or logarithmic forms involving square roots.
What are the signs? Look at the signs of the squared variable term (like x²) and the constant term (like a²). For example, √(a² - x²) leads to a sin⁻¹(x/a) form, whereas √(x² + a²) leads to a logarithmic form.
Carefully matching this resulting structure to the standard formulas is the key to a correct solution.
6. What is the most common mistake students make while solving problems from RS Aggarwal Chapter 14?
A very common mistake is an error in the algebraic manipulation during the completing the square process. Students often miscalculate the term that needs to be added and subtracted. Another frequent error is forgetting to add the constant of integration, '+C', at the end of an indefinite integral. Forgetting '+C' can lead to a loss of marks in the CBSE board exams.
7. How do the RS Aggarwal Class 12 solutions for Some Special Integrals help in preparing for the board exams?
These solutions are highly beneficial for board exam preparation as per the CBSE 2025-26 syllabus. They provide:
Step-by-step methods: Clear, sequential steps for every problem, which is exactly how answers should be written in the exam for full marks.
Variety of problems: RS Aggarwal provides extensive practice on all variations of special integrals, ensuring you are prepared for any question type.
Clarity on formulas: By solving numerous questions, you gain a solid understanding of when and how to apply each of the nine special integral formulas.
8. Where can I find accurate and detailed solutions for all exercises in RS Aggarwal Class 12 Maths Chapter 14?
Vedantu provides meticulously crafted, 100% accurate solutions for every single question in RS Aggarwal Class 12 Maths Chapter 14, Some Special Integrals. These solutions are prepared by expert Maths teachers and follow the CBSE guidelines for the 2025-26 session, ensuring you learn the correct methods to score high marks in your examinations.
