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The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-
- a)(x-1) cos (3x + 4)
- b)sin (3x + 4)
- c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)
- d)sin (3x + 4) + (x – 1) cos (3x + 4)
Correct answer is option 'C'. Can you explain this answer?
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The area bounded by curves y = f(x), the x-axis and the ordinates x = ...
1. Area bounded by curve y = f(x), x =1 and x = b is
Now differentiating both sides with respect to b we get
fB. = sin (3b + 4) + 3(b – 1) cos (3b + 4)
Now differentiating both sides with respect to b we get
fB. = sin (3b + 4) + 3(b – 1) cos (3b + 4)
Most Upvoted Answer
The area bounded by curves y = f(x), the x-axis and the ordinates x = ...
The correct answer is c) sin(3x - 4).
To find the area bounded by the curves y = f(x), the x-axis, and the ordinates x = 1 and x = b, we need to integrate the function f(x) over the interval [1, b].
The formula for the area bounded by a curve y = f(x) and the x-axis over the interval [a, b] is given by the definite integral:
Area = ∫[a, b] f(x) dx
In this case, the given area is (b - 1) sin(3b - 4). Therefore, we need to find a function f(x) such that:
∫[1, b] f(x) dx = (b - 1) sin(3b - 4)
Taking the derivative of both sides with respect to x, we get:
f(x) = d/dx [(b - 1) sin(3b - 4)]
Using the chain rule, the derivative of (b - 1) sin(3b - 4) with respect to x is:
f(x) = (b - 1) cos(3b - 4) * d/dx (3b - 4)
Since d/dx (3b - 4) = 3, we can simplify the expression further:
f(x) = (b - 1) cos(3b - 4) * 3
Simplifying, we get:
f(x) = 3(b - 1) cos(3b - 4)
However, this does not match any of the answer choices. Therefore, the given information is either incorrect or incomplete, and we cannot determine the exact function f(x) with the given information.
To find the area bounded by the curves y = f(x), the x-axis, and the ordinates x = 1 and x = b, we need to integrate the function f(x) over the interval [1, b].
The formula for the area bounded by a curve y = f(x) and the x-axis over the interval [a, b] is given by the definite integral:
Area = ∫[a, b] f(x) dx
In this case, the given area is (b - 1) sin(3b - 4). Therefore, we need to find a function f(x) such that:
∫[1, b] f(x) dx = (b - 1) sin(3b - 4)
Taking the derivative of both sides with respect to x, we get:
f(x) = d/dx [(b - 1) sin(3b - 4)]
Using the chain rule, the derivative of (b - 1) sin(3b - 4) with respect to x is:
f(x) = (b - 1) cos(3b - 4) * d/dx (3b - 4)
Since d/dx (3b - 4) = 3, we can simplify the expression further:
f(x) = (b - 1) cos(3b - 4) * 3
Simplifying, we get:
f(x) = 3(b - 1) cos(3b - 4)
However, this does not match any of the answer choices. Therefore, the given information is either incorrect or incomplete, and we cannot determine the exact function f(x) with the given information.
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The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer?
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The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer?.
The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer?.
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The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The area bounded by curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4). Then f(x) is-a)(x-1) cos (3x + 4)b)sin (3x + 4)c)sin (3x + 4) + 3 (x – 1) cos (3x + 4)d)sin (3x + 4) + (x – 1) cos (3x + 4)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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