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Find the area of the region bounded by the curve y2 = 4x and x2 = 4y.

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Given curves are y2 = 4x … (i) and x2 = 4y … (ii)

On solving the equations, we get

From (ii),

y = x2/4

Putting value of y in (i), we have

(x2/4)2 = 4x

x4/16 = 4x

x4 = 64x

x4 – 64x = 0

So, x = 0, 4

Now, the required area is the shaded region

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