Q24 of 21 Page 8

Using integration, find the area of the region: {(x, y): 0 ≤ 2y ≤ x2 , 0 ≤ y ≤ x, 0 < x < 3}. [CBSE 2018(C)]

Let us calculate the points of intersection of x2 = 2y and y = x
Putting y = x in x2 = 2y, we get,
y2 = 2y
y2 - 2y = 0
y(y - 2) = 0
y = 0 or y = 2
And as y = x, x = 0 or x = 2
Points of intersection are (0, 0) and (2, 2)



we know that,

Applying the formula, we get,

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