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The area enclosed between the straight line y = x and the parabola y = x² in the x–y plane is
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- 1/6
- 1/4
- 1/3
- 1/2
Correct Option: A
Given equations are y = x² ...(i)
y = x ...(ii)
From equations (i) and (ii)
x² – x = 0
→ x(x – 1) = 0
→ x = 0, 1
Area enclosed
= 1∫x=0y=x³∫y=xdy dx1∫x=0 dxy=x²∫y=x dy
= 1∫x=0[y]²x dx = 1∫x=0(x² - x)dx
| = |  | - |  | 1 | = | - | = | = - | ||||||
| 3 | 2 | 0 | 3 | 2 | 6 | 6 |
| ∴ Enclosed area = |  | - | | = | ||
| 6 | 6 |
