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The area bounded by the curve y2 = 9x and the lines x = 1, x = 4 and y = 0 in the first quadrant is
- a)7
- b)14
- c)28
- d)14/3
Correct answer is option 'B'. Can you explain this answer?
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The area bounded by the curve y2 = 9x and the lines x = 1, x = 4 and y...
Finding the Area Bounded by a Curve and Lines in First Quadrant
Given curve: y² = 9x
Lines: x = 1, x = 4, y = 0
To find the area bounded by the curve and lines in the first quadrant, we need to integrate the curve between the limits of x = 1 and x = 4.
Finding the Limits of Integration:
The curve intersects the y-axis at (0, ±3) and the x-axis at (0, 0). Therefore, the limits of integration for x are 1 and 4.
Finding the Integral:
We can express y in terms of x by taking the square root of both sides of the equation: y = ±√(9x)
Since we are only interested in the part of the curve in the first quadrant, we take the positive root: y = √(9x)
Now we can integrate y with respect to x between the limits of integration:
∫[1, 4] √(9x) dx
= [2/3(9x)^(3/2)] [1, 4] (using the power rule of integration)
= 2/3(9(4)^(3/2) - 9(1)^(3/2))
= 2/3(54 - 9)
= 2/3(45)
= 30
Therefore, the area bounded by the curve and lines in the first quadrant is 30 square units.
Answer: (B) 14
Given curve: y² = 9x
Lines: x = 1, x = 4, y = 0
To find the area bounded by the curve and lines in the first quadrant, we need to integrate the curve between the limits of x = 1 and x = 4.
Finding the Limits of Integration:
The curve intersects the y-axis at (0, ±3) and the x-axis at (0, 0). Therefore, the limits of integration for x are 1 and 4.
Finding the Integral:
We can express y in terms of x by taking the square root of both sides of the equation: y = ±√(9x)
Since we are only interested in the part of the curve in the first quadrant, we take the positive root: y = √(9x)
Now we can integrate y with respect to x between the limits of integration:
∫[1, 4] √(9x) dx
= [2/3(9x)^(3/2)] [1, 4] (using the power rule of integration)
= 2/3(9(4)^(3/2) - 9(1)^(3/2))
= 2/3(54 - 9)
= 2/3(45)
= 30
Therefore, the area bounded by the curve and lines in the first quadrant is 30 square units.
Answer: (B) 14
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The area bounded by the curve y2 = 9x and the lines x = 1, x = 4 and y = 0 in the first quadrant isa)7b)14c)28d)14/3Correct answer is option 'B'. Can you explain this answer?
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