JEE Exam > JEE Questions > The area of the region bounded by the curves ...
Start Learning for Free
The area of the region bounded by the curves y = |x-1| and y = 3-|x| is
- a)3 sq. units
- b)4 sq. units
- c)6 sq. units
- d)2 sq. units
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The area of the region bounded by the curves y = |x-1| and y = 3-|x| i...
To find the area of the region bounded by the curves y = |x-1| and y = 3-|x|, we need to determine the points of intersection of these two curves and then calculate the area between them.
Step 1: Finding the Points of Intersection
To find the points of intersection, we set the two equations equal to each other:
|x-1| = 3-|x|
To simplify the equation, we break it into two cases based on the absolute value:
Case 1: (x-1) = (3-x)
Simplifying this equation gives us:
2x = 4
x = 2
Case 2: -(x-1) = 3-|x|
Simplifying this equation gives us:
-x + 1 = 3 - x
1 = 3
This case does not yield a valid solution.
So, the only point of intersection is x = 2.
Step 2: Calculating the Area
To calculate the area between the curves, we integrate the difference between the two curves with respect to x over the interval [0, 2]:
Area = ∫(3-|x|) - |x-1| dx (from x = 0 to x = 2)
We break the integral into two separate integrals to account for the absolute values:
Area = ∫(3-x) - (x-1) dx (from x = 0 to x = 2)
= ∫(4-2x) dx (from x = 0 to x = 2)
= [4x-x^2] (from x = 0 to x = 2)
= [8-4-0] - [0-0-0]
= 4
Therefore, the area of the region bounded by the curves y = |x-1| and y = 3-|x| is 4 square units, which corresponds to option B.
Step 1: Finding the Points of Intersection
To find the points of intersection, we set the two equations equal to each other:
|x-1| = 3-|x|
To simplify the equation, we break it into two cases based on the absolute value:
Case 1: (x-1) = (3-x)
Simplifying this equation gives us:
2x = 4
x = 2
Case 2: -(x-1) = 3-|x|
Simplifying this equation gives us:
-x + 1 = 3 - x
1 = 3
This case does not yield a valid solution.
So, the only point of intersection is x = 2.
Step 2: Calculating the Area
To calculate the area between the curves, we integrate the difference between the two curves with respect to x over the interval [0, 2]:
Area = ∫(3-|x|) - |x-1| dx (from x = 0 to x = 2)
We break the integral into two separate integrals to account for the absolute values:
Area = ∫(3-x) - (x-1) dx (from x = 0 to x = 2)
= ∫(4-2x) dx (from x = 0 to x = 2)
= [4x-x^2] (from x = 0 to x = 2)
= [8-4-0] - [0-0-0]
= 4
Therefore, the area of the region bounded by the curves y = |x-1| and y = 3-|x| is 4 square units, which corresponds to option B.
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 of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer?
Question Description
The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. 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 of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. 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 of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer?.
The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. 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 of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. 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 of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. 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 of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The area of the region bounded by the curves y = |x-1| and y = 3-|x| isa)3 sq. unitsb)4 sq. unitsc)6 sq. unitsd)2 sq. unitsCorrect answer is option 'B'. 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