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The area bounded by the parabola x = 4 − y2 and the y-axis, in square units is
- a)3/32
- b)32/3
- c)33/2
- d)16/3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The area bounded by the parabola x = 4 − y2 and the y-axis, in s...
Explanation:
The given parabola is x = 4 - y^2.
Finding the points of intersection:
To find the points of intersection with the y-axis, we set x = 0:
0 = 4 - y^2
y^2 = 4
y = ±2
So, the parabola intersects the y-axis at y = 2 and y = -2.
Finding the area:
To find the area bounded by the parabola and the y-axis, we integrate the absolute value of the function between the y-values of intersection points:
Area = ∫[from -2 to 2] |x| dy
= ∫[from -2 to 2] |4 - y^2| dy
= ∫[from -2 to 2] |4 - y^2| dy
= 2 ∫[from 0 to 2] (4 - y^2) dy
= 2 [4y - (y^3)/3] [from 0 to 2]
= 2 [8 - 8/3]
= 2 * (24/3 - 8/3)
= 2 * 16/3
= 32/3 square units
Therefore, the area bounded by the parabola x = 4 - y^2 and the y-axis is 32/3 square units. Hence, option B is correct.
The given parabola is x = 4 - y^2.
Finding the points of intersection:
To find the points of intersection with the y-axis, we set x = 0:
0 = 4 - y^2
y^2 = 4
y = ±2
So, the parabola intersects the y-axis at y = 2 and y = -2.
Finding the area:
To find the area bounded by the parabola and the y-axis, we integrate the absolute value of the function between the y-values of intersection points:
Area = ∫[from -2 to 2] |x| dy
= ∫[from -2 to 2] |4 - y^2| dy
= ∫[from -2 to 2] |4 - y^2| dy
= 2 ∫[from 0 to 2] (4 - y^2) dy
= 2 [4y - (y^3)/3] [from 0 to 2]
= 2 [8 - 8/3]
= 2 * (24/3 - 8/3)
= 2 * 16/3
= 32/3 square units
Therefore, the area bounded by the parabola x = 4 - y^2 and the y-axis is 32/3 square units. Hence, option B is correct.
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The area bounded by the parabola x = 4 − y2 and the y-axis, in square units isa)3/32b)32/3c)33/2d)16/3Correct answer is option 'B'. Can you explain this answer?
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The area bounded by the parabola x = 4 − y2 and the y-axis, in square units isa)3/32b)32/3c)33/2d)16/3Correct answer is option 'B'. 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 bounded by the parabola x = 4 − y2 and the y-axis, in square units isa)3/32b)32/3c)33/2d)16/3Correct answer is option 'B'. 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 bounded by the parabola x = 4 − y2 and the y-axis, in square units isa)3/32b)32/3c)33/2d)16/3Correct answer is option 'B'. Can you explain this answer?.
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