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The area bounded by the curve y2 = 8x and x2 = 8y is
This problem is similar to Problem 2. So we’ll solve it in a similar way.
At points of intersection,
y2 = 8x
(from the other equation)
Let us solve this.
x4 = 512x
⇒ x(x3 – 512) = 0
⇒ x = 0 or x3 = 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.