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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?
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The area lying in the first quadrant and bounded by the curve y =x3 , ...
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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.
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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?
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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?.
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