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NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.1 - Application of Integrals

NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.1 - Application of Integrals

Edited By Komal Miglani | Updated on May 08, 2025 02:32 PM IST | #CBSE Class 12th

Application of Integrals is like your favourite colouring brush that can fill any shape under every curve, no matter how abstract the shape is. It is a fundamental part of calculus that can help us calculate the area of a certain region, even with no straight sides. In exercise 8.1 of the chapter Application of Integrals, we go beyond the basics of integration and learn about how it's used in our real-life situations, like finding the area of a region or calculating the total distance travelled between two specific points. This article about the NCERT Solutions for Exercise 8.1 of Class 12 Maths, Chapter 8 - Application of Integrals, offers detailed and easy-to-understand solutions for the exercise problems, so that students can clear their doubts and understand the logic behind the solutions. For syllabus, notes, exemplar solutions and PDF, refer to this link: NCERT.

This Story also Contains
  1. Class 12 Maths Chapter 8 Exercise 8.1 Solutions: Download PDF
  2. Application of Integrals Class 12 Chapter 8 Exercise: 8.1
  3. Topics covered in Chapter 8, Application of Integrals: Exercise 8.1
  4. NCERT Solutions Subject Wise
  5. NCERT Exemplar Solutions Subject Wise
LiveCBSE Result 2025 (LIVE): Class 10, 12 marksheet likely today at cbse.gov.in, Digilocker; websites to checkMay 12, 2025 | 5:54 PM IST

The Central Board of Secondary Education (CBSE) has revised the process for post-result activities. Accordingly, students who feel dissatisfied with their CBSE Class 10, 12 results 2025 will have to apply for the photocopy of their answer sheets first and then only move on to get their marks verified. 

Read More: CBSE Class 10, 12 result process revised; answer book photocopy now comes before re-evaluation

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Class 12 Maths Chapter 8 Exercise 8.1 Solutions: Download PDF

Download PDF

Application of Integrals Class 12 Chapter 8 Exercise: 8.1

Question:1 Find the area of the region bounded by the ellipse x216+y29=1.

Answer:

The area bounded by the ellipse : x216+y29=1.

1654756804735

Area will be 4 times the area of EAB.

Therefore, Area of EAB = ∫04ydx

=∫0431−x216dx

=34∫0416−x2dx

=34[x216−x2+162sin−1⁡x4]04

=34[216−16+8sin−1⁡(1)−0−8sin−1⁡(0)]

=34[8π2]

=34[4π]=3π

Therefore, the area bounded by the ellipse will be =4×3π=12π units.

Question 2: Find the area of the region bounded by the ellipse x24+y29=1

Answer:

The area bounded by the ellipse : x24+y29=1

1654756868830

The area will be 4 times the area of EAB.

Therefore, Area of EAB =∫02y dx

=∫0231−x24dx

=32∫024−x2dx

=32[x24−x2+42sin−1⁡x2]02

=32[2π2]

=3π2

Therefore the area bounded by the ellipse will be =4×3π2=6π units.

Question 3: Choose the correct answer in the following

Area lying in the first quadrant and bounded by the circle x2+y2=4 and the lines x=0 and x=2 is

(A)π

(B)π2

(C)π3

(D)π4

Answer:
The area bounded by circle C(0,0,4) and the line x=2 is

1745483267490

The required area = area of OAB

∫02ydx=∫024−x2dx

=[x24−x2+42sin−1⁡x2]02

=2⋅π2

=π

Hence, The correct answer is π

Question 4: Choose the correct answer in the following.

Area of the region bounded by the curve y2=4x , y -axis and the line y=3 is

(A) 2

(B) 94

(C) 93

(D) 92

Answer:

The area bounded by the curve y2=4x and y =3

1745483395032

The required area = OAB

=∫03xdy

=∫03y24dy

=14[y33]03

=94

Hence, The correct answer is 94


Also Read,

Background wave

Topics covered in Chapter 8, Application of Integrals: Exercise 8.1

The main topic covered in class 12 maths chapter 8 of Application of Integrals, exercise 8.1 is:

Area under a curve: The exercise starts with calculating the area under the curve y=f(x), between two points on the X axis, as x=a and x=b. The area can be found using definite integrals as: A=∫abf(x)dx.

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NCERT Solutions Subject Wise

Below are some useful links for subject-wise NCERT solutions for class 12.

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NCERT Exemplar Solutions Subject Wise

Here are some links to subject-wise solutions for the NCERT exemplar class 12.

JEE Main Important Mathematics Formulas

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

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Frequently Asked Questions (FAQs)

1. How many questions are there in exercise 8.1 Class 12 Maths ?

13 questions are in total in exercise 8.1 Class 12 Maths.

2. Which applications are mentioned in this exercise ?

Mainly area under the curve is discussed in this exercise.

3. Is this chapter very important for Board exams ?

This is very important for boards as well as other subjects like Physics also. 

4. Is it more difficult than the previous chapter ?

No, it is less difficult than Chapter 7 Integrals. 

5. What are some other topics discussed in this Chapter ?

Maily area and at higher level volume etc. are discussed in this.

6. How many exercises are there in this Chapter ?

Total 3 exercises are there including miscellaneous exercise.

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Can I change my board from CBSE to CHSE Odisha in Class 12th?

Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.

Read Complete Answer
Manasvini Gupta 30 January,2025
quartely question paper for mathematics cbse

Hello there! Thanks for reaching out to us at Careers360.

Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.

Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!

Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.

If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.

Let me know if you need any other tips for your math prep. Good luck with your studies!

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Jefferson 25 September,2024
i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

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I hope this information helps you.







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Kanishka kaushikii 17 September,2024
i scored 84 percent in cbse 2 years ago.Am i eligible for medhavi scholarship if give 12th again after 2 drop years and will got 75+ in mpboard

Hi,

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Yuvan 30 August,2024
i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

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Ashvadha 12 July,2024
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