The area bounded by the curve y^{2} = 8x and x^{2} = 8y is

This problem is similar to Problem 2. So we’ll solve it in a similar way.

At points of intersection,

y^{2} = 8x

(from the other equation)

Let us solve this.

x^{4} = 512x

⇒ x(x^{3} – 512) = 0

⇒ x = 0 or x^{3} = 512, i.e, x = 8

So the points of intersection are (0,0) and (8,8)

Now, let’s compute the area.

If we integrate w.r.t x, we’ll have to integrate the space between the two curves from x = 0 to x = 8.

i.e.,

(Ans)

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