JEE Exam > JEE Questions > The area enclosed between the curves y = ax2 ...
Start Learning for Free
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a is
- a)1/√3
- b)1/2
- c)1
- d)1/3
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is...
y = ax2 and x = ay2
Points of intersection are O (0, 0) and
Most Upvoted Answer
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is...
We need to find the points of intersection between the two curves in order to determine the boundaries of the enclosed area.
Setting y = ax^2 and x = ay^2, we have:
ay^2 = a(x/a)^2
Simplifying, we get:
y^2 = x/a
x = ay^2 = a(ax^2)^2 = a^3x^4
Therefore, the points of intersection are (0,0) and (a^2,a^3).
To find the area enclosed between the curves, we integrate the difference between the two functions with respect to x, from x = 0 to x = a^2:
A = ∫[0,a^2] (ax^2 - ay^2) dx
= a ∫[0,a^2] (x^2 - y^2) dx
= a [x^3/3 - xy^2/2] [0,a^2]
= a (a^6/3 - a^6/2)
= a^7/6
Therefore, the area enclosed between the curves y = ax^2 and x = ay^2 is a^7/6.
Setting y = ax^2 and x = ay^2, we have:
ay^2 = a(x/a)^2
Simplifying, we get:
y^2 = x/a
x = ay^2 = a(ax^2)^2 = a^3x^4
Therefore, the points of intersection are (0,0) and (a^2,a^3).
To find the area enclosed between the curves, we integrate the difference between the two functions with respect to x, from x = 0 to x = a^2:
A = ∫[0,a^2] (ax^2 - ay^2) dx
= a ∫[0,a^2] (x^2 - y^2) dx
= a [x^3/3 - xy^2/2] [0,a^2]
= a (a^6/3 - a^6/2)
= a^7/6
Therefore, the area enclosed between the curves y = ax^2 and x = ay^2 is a^7/6.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer?
Question Description
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer?.
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer?.
Solutions for The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit, then the value of a isa)1/√3b)1/2c)1d)1/3Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup