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The area of the region bounded by the curves y = |x – 1| and y = 3 – |x| is :
- a)3 sq. units
- b)6 sq. units
- c)2 sq. units
- d)4 sq. units
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The area of the region bounded by the curvesy= |x– 1| andy= 3 &n...
The required area can be divided into, three regions
= 2 – 1 + 2 + 8 – 4 – 4 +1
= 4 sq. units
The correct answer is: 4 sq. units
Most Upvoted Answer
The area of the region bounded by the curvesy= |x– 1| andy= 3 &n...
The area of the region bounded by the curve y = |x| can be found by splitting the region into two parts: the region above the x-axis and the region below the x-axis.
1) Region above the x-axis:
In this region, the equation of the curve is y = x. To find the x-coordinate where the curve intersects the x-axis, we set y = 0 and solve for x:
0 = x
x = 0
So the curve intersects the x-axis at x = 0. The area of this region can be found by integrating the equation y = x from x = 0 to the x-coordinate where it intersects the curve y = |x|, which is also at x = 0.
∫[0, 0] x dx = 0
Therefore, the area of the region above the x-axis is 0.
2) Region below the x-axis:
In this region, the equation of the curve is y = -x. To find the x-coordinate where the curve intersects the x-axis, we set y = 0 and solve for x:
0 = -x
x = 0
So the curve intersects the x-axis at x = 0. The area of this region can be found by integrating the equation y = -x from x = 0 to the x-coordinate where it intersects the curve y = |x|, which is also at x = 0.
∫[0, 0] -x dx = 0
Therefore, the area of the region below the x-axis is 0.
In conclusion, the area of the region bounded by the curve y = |x| is 0.
1) Region above the x-axis:
In this region, the equation of the curve is y = x. To find the x-coordinate where the curve intersects the x-axis, we set y = 0 and solve for x:
0 = x
x = 0
So the curve intersects the x-axis at x = 0. The area of this region can be found by integrating the equation y = x from x = 0 to the x-coordinate where it intersects the curve y = |x|, which is also at x = 0.
∫[0, 0] x dx = 0
Therefore, the area of the region above the x-axis is 0.
2) Region below the x-axis:
In this region, the equation of the curve is y = -x. To find the x-coordinate where the curve intersects the x-axis, we set y = 0 and solve for x:
0 = -x
x = 0
So the curve intersects the x-axis at x = 0. The area of this region can be found by integrating the equation y = -x from x = 0 to the x-coordinate where it intersects the curve y = |x|, which is also at x = 0.
∫[0, 0] -x dx = 0
Therefore, the area of the region below the x-axis is 0.
In conclusion, the area of the region bounded by the curve y = |x| is 0.
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The area of the region bounded by the curvesy= |x– 1| andy= 3 – |x| is :a)3 sq. unitsb)6 sq. unitsc)2 sq. unitsd)4 sq. unitsCorrect answer is option 'D'. Can you explain this answer?
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