JEE Exam > JEE Questions > The area lying in the first quadrant and boun...
Start Learning for Free
The area lying in the first quadrant and bounded by the curve y = x3 , the x – axis and the ordinates at x = - 2 and x = 1 is
- a)6
- b)3
- c)15/4
- d)2
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The area lying in the first quadrant and bounded by the curve y =x3 , ...
Required area :
Most Upvoted Answer
The area lying in the first quadrant and bounded by the curve y =x3 , ...
Given Information:
The area bounded by the curve y = x^3, the x-axis, and the ordinates at x = -2 and x = 1 in the first quadrant needs to be calculated.
Approach to Solution:
To find the area of the region bounded by the curve, x-axis, and the given ordinates, we need to integrate the function y = x^3 with respect to x over the interval [-2, 1].
Calculation:
The area A is given by the integral of the function y = x^3 over the interval [-2, 1]:
A = ∫[from -2 to 1] x^3 dx
Integrating x^3 with respect to x, we get:
A = [x^4/4] |_(-2)^(1)
Now, substitute the limits of integration and solve:
A = (1^4/4) - ((-2)^4/4)
A = 1/4 - 16/4
A = -15/4
However, since we are interested in the area in the first quadrant, we take the absolute value of the result:
Area = |A| = |-15/4| = 15/4
Therefore, the area lying in the first quadrant and bounded by the curve y = x^3, the x-axis, and the ordinates at x = -2 and x = 1 is 15/4. Hence, the correct answer is option C.
The area bounded by the curve y = x^3, the x-axis, and the ordinates at x = -2 and x = 1 in the first quadrant needs to be calculated.
Approach to Solution:
To find the area of the region bounded by the curve, x-axis, and the given ordinates, we need to integrate the function y = x^3 with respect to x over the interval [-2, 1].
Calculation:
The area A is given by the integral of the function y = x^3 over the interval [-2, 1]:
A = ∫[from -2 to 1] x^3 dx
Integrating x^3 with respect to x, we get:
A = [x^4/4] |_(-2)^(1)
Now, substitute the limits of integration and solve:
A = (1^4/4) - ((-2)^4/4)
A = 1/4 - 16/4
A = -15/4
However, since we are interested in the area in the first quadrant, we take the absolute value of the result:
Area = |A| = |-15/4| = 15/4
Therefore, the area lying in the first quadrant and bounded by the curve y = x^3, the x-axis, and the ordinates at x = -2 and x = 1 is 15/4. Hence, the correct answer is option C.
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
|
|
Top Courses for JEEView all
The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer?
Question Description
The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. 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 lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. 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 lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer?.
The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. 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 lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. 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 lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer?.
Solutions for The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. 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 lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The area lying in the first quadrant and bounded by the curve y =x3 , the x – axis and the ordinates at x = - 2 and x = 1 isa)6b)3c)15/4d)2Correct answer is option 'C'. 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