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NCERT Solutions for Exercise 8.1 Class 12 Maths Chapter 8 Application of Integrals are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for Class 12 Maths chapter 8 exercise 8.1 is the extension of last chapter i.e integrals. Concepts learnt in Class 12 Maths NCERT book chapter Integrals will be used heavily in this chapter. Exercise 8. Class 12 Maths deals with area finding of simple curves. NCERT solutions for Class 12 Maths chapter 8 exercise 8.1 requires only basic understanding of integrals which is learnt in the NCERT book previous chapter.
Similar questions are asked in Physics also, hence this NCERT syllabus exercise becomes more important. Upcoming exercises are also linked to this exercise, hence sincerely it should be practice. 12th class Maths exercise 8.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
Question:1 Find the area of the region bounded by the curve and the lines and the -axis in the first quadrant.
Answer:
Area of the region bounded by the curve and the lines and the -axis in the first quadrant
Area =
= 14/3 units
Question:2 Find the area of the region bounded by and the -axis in the first quadrant.
Answer:
Area of the region bounded by the curve and the -axis in the first quadrant
Area =
units
Question:3 Find the area of the region bounded by and the -axis in the first quadrant.
Answer:
The area bounded by the curves and the -axis in the first quadrant is ABCD.
Question:4 Find the area of the region bounded by the ellipse
Answer:
The area bounded by the ellipse :
Area will be 4 times the area of EAB.
Therefore,
Therefore the area bounded by the ellipse will be
Question: 5 Find the area of the region bounded by the ellipse
Answer:
The area bounded by the ellipse :
The area will be 4 times the area of EAB.
Therefore,
Therefore the area bounded by the ellipse will be
Question: 6 Find the area of the region in the first quadrant enclosed by -axis, line and the circle
Answer:
The area of the region bounded by and is ABC shown:
The point B of the intersection of the line and the circle in the first quadrant is .
Area ABC = Area ABM + Area BMC where, M is point in x-axis perpendicular drawn from the line.
Now,area of ............(1)
and Area of
..................................(2)
then adding the area (1) and (2), we have then
The Area under ABC
Question: 7 Find the area of the smaller part of the circle cut off by the line
Answer:
we need to find the area of smaller part of the circle
Now,
Area of ABCD = 2 X Area of ABC
Area of ABC =
Area of ABCD = 2 X Area of ABC
Therefore, the area of the smaller part of the circle is
Question:8 The area between and is divided into two equal parts by the line , find the value of .
Answer:
we can clearly see that given area is symmetrical about x - axis
It is given that
Area of OED = Area of EFCD
Area of OED =
Area of EFCD =
Area of OED = Area of EFCD
Therefore, the value of a is
Question:9 Find the area of the region bounded by the parabola and .
Answer:
We can clearly see that given area is symmetrical about y-axis
Therefore,
Area of OCAO = Area of OBDO
Point of intersection of is (1 , 1) and (-1 , 1)
Now,
Area od OCAO = Area OAM - Area of OCMO
Area of OAM =
Area of OCMO =
Therefore,
Area od OCAO
Now,
Area of the region bounded by the parabola and is = 2 X Area od OCAO Units
Question: 10 Find the area bounded by the curve and the line .
Answer:
Points of intersections of is
Now,
Area of OBAO = Area of OBCO + Area of OCAO
Area of OBCO = Area of OMBCO- Area of OMBO
Area of OMBCO =
Area of OMBO =
Area of OBCO = Area of OMBCO- Area of OMBO
Similarly,
Area of OCAO = Area of OCALO - Area of OALO
Area of OCALO =
Area of OALO =
Area of OCAO = Area of OCALO - Area of OALO
Now,
Area of OBAO = Area of OBCO + Area of OCAO
Therefore, area bounded by the curve and the line is
Question: 11 Find the area of the region bounded by the curve and the line .
Answer:
The combined figure of the curve and
The required are is OABCO, and it is symmetrical about the horizontal axis.
Therefore, Area of OABCO = 2 Area of OAB
therefore the required area is units.
Question: 12 Choose the correct answer in the following
Area lying in the first quadrant and bounded by the circle and the lines and is
Answer:
The correct answer is A
The area bounded by circle C(0,0,4) and the line x=2 is
The required area = area of OAB
Question: 13 Choose the correct answer in the following.
Area of the region bounded by the curve , -axis and the line is
(A) (B) (C) (D)
Answer:
The area bounded by the curve and y =3
the required area = OAB =
The NCERT Class 12 Maths chapter Application of Integrals mainly deals with the finding out of area, volume etc. Exercise 8.1 Class 12 Maths is the extension and application of everything learnt in chapter 7. Hence before doing NCERT Solutions for Class 12 Maths chapter 8 exercise 8.1 one should complete chapter 7 Integrals.
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Happy learning!!!
13 questions are in total in exercise 8.1 Class 12 Maths.
Mainly area under the curve is discussed in this exercise.
This is very important for boards as well as other subjects like Physics also.
No, it is less difficult than Chapter 7 Integrals.
Maily area and at higher level volume etc. are discussed in this.
Total 3 exercises are there including miscellaneous exercise.
Application Date:05 September,2024 - 04 October,2024
Application Date:05 September,2024 - 04 October,2024
Application Date:09 September,2024 - 14 November,2024
Application Date:09 September,2024 - 14 November,2024
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!
It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.
Possible steps:
Re-evaluate Your Study Strategies:
Consider Professional Help:
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Focus on NEET 2025 Preparation:
Seek Support:
Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.
I hope this information helps you.
Hi,
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Scholarships can range from Rs. 2,000 to Rs. 18,000 per month, depending on the marks obtained and the type of scholarship exam (SAKSHAM, SWABHIMAN, SAMADHAN, etc.).
Since you already have a 12th grade qualification with 84%, you meet the qualification criteria and are eligible to apply for the Medhavi Scholarship exam. Make sure to prepare well for the exam to maximize your chances of receiving a higher scholarship.
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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.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
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