I=∫_0^1√(x(1 x))dx ∫√(x(1 x)) dx= ∫ (x x^2)dx =x^22 x^33+C Therefore, I=12 13 0=16 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Property 2

∫10√x1-xdx

Question

$\int_{0}^{1} \sqrt{x (1 - x)} d x$

Open in App

Solution

$I = 1 \int 0 \sqrt{x (1 - x)} d x$
$\int \sqrt{x (1 - x)} d x = \int (x - x^{2}) d x$
$= \frac{x^{2}}{2} - \frac{x^{3}}{3} + C$

Therefore,
$I = \frac{1}{2} - \frac{1}{3} - 0 = \frac{1}{6}$

Suggest Corrections

Similar questions

\int x \sqrt{\frac{1 - x}{1 + x}} d x

\int_{- 1}^{1} x (1 - x) (1 + x) d x

\int \frac{1}{\sqrt{x} (1 + \sqrt{x})} d x =

\int_{0}^{1} \sqrt{x (1 - x)} d x =

\int \frac{1}{\sqrt{x} (1 + x)} d x

Join BYJU'S Learning Program