The area between x = y² and x = 4 is divided into two equal parts by the line x = a, find the value of a.

Open in App

Solution

The line, x = a, divides the area bounded by the parabola and x = 4 into two equal parts.

∴ Area OAD = Area ABCD

It can be observed that the given area is symmetrical about x-axis.

⇒ Area OED = Area EFCD

$Area OED= \int_{0}^{a} y ⅆ x = \int_{0}^{a} \sqrt{x} ⅆ x = {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{0}^{a} = \frac{2}{3} (a)^{\frac{3}{2}} ... (1) Area of EFCD= \int_{a}^{4} \sqrt{x} ⅆ x = [\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]_{a}^{4} = \frac{2}{3} [8 - a^{\frac{3}{2}}] ... (2)$

From (1) and (2), we obtain

Therefore, the value of a is .

Suggest Corrections

Similar questions

The area between $x = y^{2}$ and x = 4 is divided into two equal parts by the line x = a, find the value of a.

y^{2} = x

f (x) = x^{3}

x = 0

x = 4

x = K

K^{2}

A (4, 0)

y = \sqrt{2} sin (π x / 4)

x

x = 2

x = 4

Join BYJU'S Learning Program