Question

Area enclosed between the curve y² (2a – x) = x³ and the line x = 2a above x-axis is

A. \(\pi a^2\)

B. \(\frac{3}{2}\pi a^2\)

C. 2π a²

D. 3π a²

Answer 1

Correct answer is B.

Since we are concerned with the area above the x – axis, we’ll be considering the positive root.

We can see that at x = 0, y = 0.

So,

Putting √x = u

We get du = (1/2√x)dx

or, dx = 2u du

So,

Putting u = √2√a sin t

We get du = √2√a cos t dt