An Overview of Ncert Books Class 12 Maths Chapter 8 Free Download
FAQs on Ncert Books Class 12 Maths Chapter 8 Free Download
1. What are the most important types of questions from Chapter 8, Application of Integrals, for the Class 12 Board Exam 2025-26?
For the CBSE 2025-26 exam, the most expected questions involve finding the area of regions bounded by simple curves. Key types include:
- Area under a single curve (parabola, circle, ellipse) and a coordinate axis.
- Area of the region bounded by a curve and a line.
- Area of the region bounded by two distinct curves (e.g., two parabolas or a circle and a parabola).
2. What is the typical marks weightage for Application of Integrals in the CBSE Class 12 Maths exam?
As per recent board trends, Chapter 8 (Application of Integrals) usually carries a weightage of around 4 to 6 marks. This often consists of one Long Answer (LA) type question, making proficiency in this chapter crucial for scoring well.
3. Are Multiple Choice Questions (MCQs) expected from Chapter 8, and what concepts do they typically test?
Yes, you can expect 1-mark MCQs or very short answer questions from this chapter. These questions typically test your understanding of the fundamental concepts, such as identifying the correct integral expression for a given shaded region or calculating the area of a very simple region bounded by a line and axes without complex calculations.
4. Why is drawing a rough sketch considered a crucial first step for solving important questions from this chapter?
Drawing a rough sketch is essential because it provides a clear visual representation of the problem. It helps you to:
- Correctly identify the required bounded region.
- Determine the upper and lower curves (or right and left curves).
- Find the accurate points of intersection, which serve as the limits of integration.
5. What is a common mistake to avoid when solving a 5-mark question involving the area between two curves?
A very common mistake is incorrectly setting up the integral. Students often forget to subtract the area of the lower curve from the area of the upper curve. The correct setup is ∫ [f(x) - g(x)] dx, where f(x) is the upper curve and g(x) is the lower curve over the specified interval. Another frequent error is miscalculating the intersection points.
6. How should I decide whether to integrate with respect to 'x' or 'y' to find the area?
The choice depends on which orientation simplifies the problem.
- Integrate with respect to 'x' (using a vertical strip) if the region has a clearly defined upper and lower boundary function. The formula is Area = ∫ y dx.
- Integrate with respect to 'y' (using a horizontal strip) if the region has a clearly defined right and left boundary function. The formula is Area = ∫ x dy.
7. For a Higher Order Thinking Skills (HOTS) question, how might the concept of area be tested differently?
HOTS questions from this chapter move beyond simple curves. They might ask you to find the area of a region bounded by three intersecting lines, or a region bounded by a curve and a tangent to it. They may also ask to find a parameter 'a' if the area bounded by a curve y = f(x,a) and a line is given. These questions test your ability to decompose complex regions and apply integration concepts accurately.
8. Which specific curves from the NCERT syllabus are most frequently featured in board exam questions?
Based on past papers, you must be extremely comfortable with sketching and finding the area related to the standard forms of:
- Parabolas: y² = 4ax, x² = 4ay
- Circles: x² + y² = a²
- Ellipses: x²/a² + y²/b² = 1
- Lines: y = mx + c or ax + by + c = 0
