NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Exercise 7.10

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Chapter 7 – Integrals Exercise 7.10

1.

Q1 Class 12 definite integration with algebraic expression under limits
Q1 setup and simplification of algebraic expression
Q1 final definite integral result under limits

2.

Q2 NCERT integral involving rational and polynomial terms
Q2 integration using partial fraction breakdown
Q2 simplified result using definite integral rule

3.

Q3 integration using substitution and limits with trigonometric function
 Q3 trig substitution used with definite limits
Q3 final result after applying identity

4.

Q4 definite integral with root and square expressions
Q4 integration of square root and square expression
Q4 Class 12 final definite value derived

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Q5 Class 12 question on applying definite integral properties
 Q5 symmetry and transformation used in evaluation

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Q6 integral using symmetry rule and rational simplification
6 rational simplification followed by integration

7.

Q7 integration question involving exponential and algebraic terms
Q7 exponential function integrated using limits

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Q8 NCERT definite integral with trigonometric product
Q8 trigonometric product simplified for integration

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Q9 integration involving identity and definite transformation
 Q9 substitution applied and trig identity used

10.

Q10 definite integral with partial fractions and simplification
Q10 partial fraction method applied in setup
Q10 evaluated result of definite integral

11.

Class-12 Integrals Exercise-7.10 Question 11 -problem on evaluating rational expressions with limits- NCERT
Class-12 Integrals Exercise-7.10 Question 11 rational expression integrated step-by-step- NCERT Answer

12.

Class-12 Integrals Exercise-7.10 Question 12 -integral requiring substitution of variable and identity
- NCERT
Class-12 Integrals Exercise-7.10 Question 12 substitution of variable used to simplify- NCERT Answer

13.

Class-12 Integrals Exercise-7.10 Question 13-integration question combining algebraic and exponential function- NCERT
Class-12 Integrals Exercise-7.10 Question 13 integration of exponential and algebraic term- NCERT Answer

14.

Class-12 Integrals Exercise-7.10 Question 14 -definite integral with logarithmic expression-NCERT
Class-12 Integrals Exercise-7.10 Question 14 logarithmic integration using definite bounds- NCERT Answer

15.

Class-12 Integrals Exercise-7.10 Question 15 -rational denominator and simplification-NCERT
Class-12 Integrals Exercise-7.10 Question 15 rational denominator simplified for integration- NCERT Answer

16.

Class-12 Integrals Exercise-7.10 Question 16-definite integral requiring square identity simplification-NCERT
Class-12 Integrals Exercise-7.10 Question 16 simplified square identity before integration- NCERT Answer
Class-12 Integrals Exercise-7.10 Question 16 answer showing full solution- NCERT Answer

17.

Class-12 Integrals Exercise-7.10 Question 17-integration of trigonometric and rational composite function-NCERT
Class-12 Integrals Exercise-7.10 Question 17 trig and rational composite function - NCERT Answer

18.

Class-12 Integrals Exercise-7.10 Question 18-integration under limits using inverse trigonometric identities-NCERT
Class-12 Integrals Exercise-7.10 Question 18 inverse trig function used in definite integration
- NCERT Answer

19.

Class-12 Integrals Exercise-7.10 Question 19 -definite integral involving standard substitution technique-NCERT
Class-12 Integrals Exercise-7.10 Question 19 standard substitution method applied- NCERT Answer

20.

Class-12 Integrals Exercise-7.10 Question 20-integration with root and rational expression-NCERT
Class-12 Integrals Exercise-7.10 Question 20 root and rational expression integrated- NCERT Answer

21.

Class-12 Integrals Exercise-7.10 Question 21-trigonometric property in integration-NCERT
Class-12 Integrals Exercise-7.10 Question 21 trigonometric identity used for definite integration- NCERT Answer

Download Exercise 7.10 NCERT Solutions PDF

You can download the PDF from the link below for offline study

Class 12 Maths Chapter 7 – Integrals: All Exercises

ExerciseLink
Exercise 7.1View Solutions
Exercise 7.2View Solutions
Exercise 7.3View Solutions
Exercise 7.4View Solutions
Exercise 7.5View Solutions
Exercise 7.6View Solutions
Exercise 7.7View Solutions
Exercise 7.8View Solutions
Exercise 7.9View Solutions
Miscellaneous ExerciseView Solutions

Class 12 Integrals- Exercise 7.10 Overview

Exercise 7.10 is the final section of Chapter 7 and is an excellent opportunity to consolidate all of the information you have acquired regarding integration. This exercise mostly concentrates on locating areas limited by curves, a useful and graphic application of definite integrals. Combining math with real-world geometry makes this section of the chapter among the most fascinating.

Mainly involving finding the area between two curves, or between a curve and the x-axis, over a given time, the challenges in Integrals Class 12 NCERT Solutions Exercise 7.10 mainly involve This advances your grasp of definite integrals from Exercises 7.7 and 7.9 and into visual learning.

The 2025 revised NCERT curriculum claims that this kind of issue is crucial in subjects including physics, engineering, architecture, and data visualization in addition to from a board test standpoint. It helps pupils to see functions graphically and to think outside of numbers and formulas.

Practicing Integrals Class 12 NCERT Solutions Exercise 7.10 can help students effectively address challenging problems including curves and areas. Not only for tests, but also for anyone hoping to work in STEM disciplines; this is a basic ability.

FAQs – Integrals Class 12 Exercise 4.1 NCERT

Could I simplify area questions in this practice using symmetry?

Indeed, if the graphs are symmetric, you can usually save time by routinely computing half the area and twice it.

What if I switch the curves by accident while taking away?

You will find a negative area. To fix it, just take the absolute value; but, it’s best to find correctly up front.

I’m not very good at drawing graphs. Is it possible for me to score high?

Certainly! Try to grasp the overall form of conventional functions—such as parabolas, lines, circles. Usually, that’s sufficient to properly establish limitations.

Does knowing how to sketch graphs help me to address these difficulties?

Indeed, knowing the limits and form of the region you are integrating helps you get at least a basic picture of the graph.

How can I determine the limits of integration at intersection of curves?

Solving the curve equations yields the points of intersection algebraically. These start to define your limits.

Is there an easier way to find the space between two curves?

Yes. Only after determining which curve is on top inside the specified interval should one use the formula Area = ∫[a to b] (Upper Curve – Lower Curve) dx.

Class 12 Maths Chapters

Chapter 1 – Relations and Functions
Chapter 2 – Inverse Trigonometric Functions
Chapter 3 – Matrices
Chapter 4 – Determinants
Chapter 5 – Continuity and Differentiability
Chapter 6 – Application of Derivatives
Chapter 7 – Integrals
Chapter 8 – Application of Integrals
Chapter 9 – Differential Equations
Chapter 10 – Vector Algebra
Chapter 11 – Three Dimensional Geometry
Chapter 12 – Linear Programming
Chapter 13 – Probability

Important Questions for Class 12