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If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4 is equals to
Correct answer is '0.25'. Can you explain this answer?
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If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4...
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If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4...
Solution:
Given curve: x |y| = 1
To find the area bounded by this curve and the y-axis, we need to determine the x-coordinate of the points where the curve intersects the y-axis.
When the curve intersects the y-axis, the x-coordinate is 0. Therefore, we need to find the corresponding y-coordinate.
To find the y-coordinate, we substitute x = 0 into the equation of the curve:
0 |y| = 1
This simplifies to:
|y| = 1
Since the absolute value of a number is always positive, the equation |y| = 1 has two solutions: y = 1 and y = -1.
So, the curve intersects the y-axis at the points (0, 1) and (0, -1).
The area bounded by the curve and the y-axis can be found by integrating the absolute value of y with respect to x from x = 0 to the x-coordinate of the point of intersection.
Let's calculate the area:
∫ |y| dx = ∫1 dx + ∫(-1) dx
Integrating both sides:
∫ |y| dx = x + C | from 0 to k
∫ |y| dx = k - 0 = k
Therefore, the area bounded by the curve and the y-axis is equal to k.
To find k/4, we divide the area by 4:
k/4 = k/4
So, the given answer of k/4 = 0.25 is correct.
Given curve: x |y| = 1
To find the area bounded by this curve and the y-axis, we need to determine the x-coordinate of the points where the curve intersects the y-axis.
When the curve intersects the y-axis, the x-coordinate is 0. Therefore, we need to find the corresponding y-coordinate.
To find the y-coordinate, we substitute x = 0 into the equation of the curve:
0 |y| = 1
This simplifies to:
|y| = 1
Since the absolute value of a number is always positive, the equation |y| = 1 has two solutions: y = 1 and y = -1.
So, the curve intersects the y-axis at the points (0, 1) and (0, -1).
The area bounded by the curve and the y-axis can be found by integrating the absolute value of y with respect to x from x = 0 to the x-coordinate of the point of intersection.
Let's calculate the area:
∫ |y| dx = ∫1 dx + ∫(-1) dx
Integrating both sides:
∫ |y| dx = x + C | from 0 to k
∫ |y| dx = k - 0 = k
Therefore, the area bounded by the curve and the y-axis is equal to k.
To find k/4, we divide the area by 4:
k/4 = k/4
So, the given answer of k/4 = 0.25 is correct.
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If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. Can you explain this answer?
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If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. 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 If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. Can you explain this answer?.
If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. 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 If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the area bounded by curve x + |y| = 1 and the y-axis is k, then k/4is equals toCorrect answer is '0.25'. Can you explain this answer?.
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