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Find the area of the region bounded by the curve y2 = 2x and x2 + y2 = 4x.

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Given equation of curves are y2 = 2and x2 + y2 = 4x

Solving the equations, we have

x– 4x + y= 0

x– 4x + 4 – 4 + y= 0

(x – 2)2 + y2 = 4

It’s clearly seen that the equation of the circle having its centre (2, 0) and radius 2.

Solving x2 + y2 = 4x and y2 = 2x

x2 + 2x = 4x

x2 + 2x – 4x = 0

x2 – 2x = 0

x(x – 2) = 0

So, x = 0, 2

Now, the area of the required region is given as

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