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The area bounded by the curves y = √x , 2y+3 = x and the x – axis in the first quadrant is
- a)9
- b)18
- c)36
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The area bounded by the curvesy = √x , 2y+3 = x and the x –...
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The area bounded by the curvesy = √x , 2y+3 = x and the x –...
Given curves:
- y = x
- 2y + 3 = x
Finding intersection points:
1. Substitute y = x into the second equation:
2( x ) + 3 = x
2x + 3 = x
x = -3
2. Substitute x = -3 into y = x:
y = -3
Intersection points:
(-3, -3)
Area calculation:
1. The area between the curves can be calculated by finding the area under the curves between the points of intersection.
2. The vertical strip of the area can be expressed as:
A = ∫[x1, x2] (f(x) - g(x)) dx
= ∫[-3, 0] (x - (2x + 3)) dx
= ∫[-3, 0] (x - 2x - 3) dx
= ∫[-3, 0] (-x - 3) dx
= [-0.5x^2 - 3x] [-3, 0]
= [4.5 - 9] = 4.5
Answer:
The area bounded by the curves y = x, 2y + 3 = x, and the x-axis in the first quadrant is 4.5 square units, which is not available in the given options. So, the correct answer is none of these.
- y = x
- 2y + 3 = x
Finding intersection points:
1. Substitute y = x into the second equation:
2( x ) + 3 = x
2x + 3 = x
x = -3
2. Substitute x = -3 into y = x:
y = -3
Intersection points:
(-3, -3)
Area calculation:
1. The area between the curves can be calculated by finding the area under the curves between the points of intersection.
2. The vertical strip of the area can be expressed as:
A = ∫[x1, x2] (f(x) - g(x)) dx
= ∫[-3, 0] (x - (2x + 3)) dx
= ∫[-3, 0] (x - 2x - 3) dx
= ∫[-3, 0] (-x - 3) dx
= [-0.5x^2 - 3x] [-3, 0]
= [4.5 - 9] = 4.5
Answer:
The area bounded by the curves y = x, 2y + 3 = x, and the x-axis in the first quadrant is 4.5 square units, which is not available in the given options. So, the correct answer is none of these.
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The area bounded by the curvesy = √x , 2y+3 = x and the x – axis in the first quadrant isa)9b)18c)36d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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