Question

Area bounded between of parabola y^2 = 9x, x^2 = 9y is

Answer 1

We have to find the area bounded by the parabola, y² = 9x and x² = 9y

Solution : let's find point of intersections.

y² = 9x and x² = 9y

x² = 9(y)

⇒x⁴ = 81y² = 81 × 9x

⇒x(x³ - 729) = 0

⇒x = 0, 9

Then, y = 0 and 9

So there are two points of intersections, (0,0) and (9,9).

So area bounded by curves = $\left|\int\limits^9_0{\left(\frac{x^2}{9}-3\sqrt{x}\right)}\,dx\right|$

= $\left[\frac{x^3}{27}-\frac{2x\sqrt{x}}{1}\right]^9_0$

= $\left[\frac{729}{27}-2(9)\sqrt{9}\right]$

= 27 [ taking absolute value of Integration ]

therefore the area enclosed by the curves y² = 9x , x² = 9y is 27 sq unit

Answer 2

Answer:

correctcorrect answer is 81/3 (mark my answer as Brainlist )