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The area of the region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis is
- a)3
- b)2
- c)1
- d)4
Correct answer is option 'C'. Can you explain this answer?
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The area of the region bounded by the curves y = |x-2|, x = 1, x = 3 a...
Area of the Region Bounded by the Curves
Given Curves:
- y = |x-2|
- x = 1
- x = 3
Step 1: Finding the Intersection Points
- To find the area of the region bounded by the curves, we first need to determine the intersection points of the curves.
- Setting y = 0 in y = |x-2| gives us x = 2 as the point of intersection.
Step 2: Determining the Region
- The region bounded by the curves is the area between the curve y = |x-2| and the x-axis from x = 1 to x = 3.
Step 3: Calculating the Area
- As the curve y = |x-2| is symmetric about x = 2, we can split the region into two parts: from x = 1 to x = 2 and from x = 2 to x = 3.
- Calculating the area under the curve from x = 1 to x = 2 gives us an area of 1.
- Similarly, calculating the area under the curve from x = 2 to x = 3 also gives us an area of 1.
- Therefore, the total area of the region bounded by the curves is 1 + 1 = 2.
Therefore, the correct answer is option C) 1.
Given Curves:
- y = |x-2|
- x = 1
- x = 3
Step 1: Finding the Intersection Points
- To find the area of the region bounded by the curves, we first need to determine the intersection points of the curves.
- Setting y = 0 in y = |x-2| gives us x = 2 as the point of intersection.
Step 2: Determining the Region
- The region bounded by the curves is the area between the curve y = |x-2| and the x-axis from x = 1 to x = 3.
Step 3: Calculating the Area
- As the curve y = |x-2| is symmetric about x = 2, we can split the region into two parts: from x = 1 to x = 2 and from x = 2 to x = 3.
- Calculating the area under the curve from x = 1 to x = 2 gives us an area of 1.
- Similarly, calculating the area under the curve from x = 2 to x = 3 also gives us an area of 1.
- Therefore, the total area of the region bounded by the curves is 1 + 1 = 2.
Therefore, the correct answer is option C) 1.
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The area of the region bounded by the curves y = |x-2|, x = 1, x = 3 and the x-axis isa)3b)2c)1d)4Correct answer is option 'C'. Can you explain this answer?
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