The area of the region bounded by parabola y2 = x and the straight line 2y = x is
Given;
Parabola y2 = x and the straight line 2y = x
By substituting for x;
⇒ y2 = 2y
⇒ y (y − 2) = 0
∴ y = 0, 2.
∴ x = 2y = 0, 4.
Required area
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The area of the region bounded by parabola y2 = x and the straight line 2y = x is
Given;
Parabola y2 = x and the straight line 2y = x
By substituting for x;
⇒ y2 = 2y
⇒ y (y − 2) = 0
∴ y = 0, 2.
∴ x = 2y = 0, 4.
Required area