JEE Exam > JEE Questions > The area, in square unit, bounded by the curv...
Start Learning for Free
The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 is
- a)17/12
- b)12/13
- c)2/7
- d)7/2
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, in square unit, bounded by the curves y = x3, y = x2 and th...
Most Upvoted Answer
The area, in square unit, bounded by the curves y = x3, y = x2 and th...
Given curves and bounds:
The given curves are y = x^3, y = x^2, and the ordinates x = 1, x = 2.
Finding the points of intersection:
To find the points of intersection, we need to solve for x when y = x^3 and y = x^2.
Setting x^3 = x^2, we get x = 0 and x = 1 as the points of intersection.
Setting up the integral:
To find the area bounded by the curves, we need to set up the integral. The area can be calculated as the difference between the curves x^3 and x^2 within the bounds of x = 1 and x = 2.
Integrating the function:
Integrating the function f(x) = x^3 - x^2 gives us F(x) = (1/4)x^4 - (1/3)x^3.
Finding the area:
Substitute the bounds x = 2 and x = 1 into the antiderivative F(x) and find the difference.
Area = F(2) - F(1) = [(1/4)(16) - (1/3)(8)] - [(1/4)(1) - (1/3)(1)] = (4 - 8/3) - (1/4 - 1/3) = 12/3 - 8/3 = 4/3 = 16/12 = 17/12.
Therefore, the area bounded by the given curves and ordinates is 17/12 square units.
The given curves are y = x^3, y = x^2, and the ordinates x = 1, x = 2.
Finding the points of intersection:
To find the points of intersection, we need to solve for x when y = x^3 and y = x^2.
Setting x^3 = x^2, we get x = 0 and x = 1 as the points of intersection.
Setting up the integral:
To find the area bounded by the curves, we need to set up the integral. The area can be calculated as the difference between the curves x^3 and x^2 within the bounds of x = 1 and x = 2.
Integrating the function:
Integrating the function f(x) = x^3 - x^2 gives us F(x) = (1/4)x^4 - (1/3)x^3.
Finding the area:
Substitute the bounds x = 2 and x = 1 into the antiderivative F(x) and find the difference.
Area = F(2) - F(1) = [(1/4)(16) - (1/3)(8)] - [(1/4)(1) - (1/3)(1)] = (4 - 8/3) - (1/4 - 1/3) = 12/3 - 8/3 = 4/3 = 16/12 = 17/12.
Therefore, the area bounded by the given curves and ordinates is 17/12 square units.
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, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer?
Question Description
The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct 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, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct 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, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer?.
The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct 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, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct 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, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer?.
Solutions for The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct 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, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 isa)17/12b)12/13c)2/7d)7/2Correct 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup