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The area enclosed between the parabala y = x2 and the straight line y = x is
- a)1/8
- b)1/6
- c)1/3
- d)1/2
Correct answer is option 'B'. Can you explain this answer?
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The area enclosed between the parabala y = x2 and the straight line ...
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The area enclosed between the parabala y = x2 and the straight line ...
Solution:
The given parabola and straight line intersect at (0,0) and (1,1).
To find the area enclosed between these two curves, we need to integrate the difference between the curves with respect to x from 0 to 1.
Area = ∫(x - x^2) dx from 0 to 1
= [x^2/2 - x^3/3] from 0 to 1
= (1/2 - 1/3)
= 1/6
Therefore, the area enclosed between the parabola y = x^2 and the straight line y = x is 1/6.
Hence, the correct answer is option B.
The given parabola and straight line intersect at (0,0) and (1,1).
To find the area enclosed between these two curves, we need to integrate the difference between the curves with respect to x from 0 to 1.
Area = ∫(x - x^2) dx from 0 to 1
= [x^2/2 - x^3/3] from 0 to 1
= (1/2 - 1/3)
= 1/6
Therefore, the area enclosed between the parabola y = x^2 and the straight line y = x is 1/6.
Hence, the correct answer is option B.
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