int frac{dx}{sqrt{x-x^2}} is equal to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $I = \int \frac{dx}{\sqrt{x-x^2}}$.We can rewrite the denominator as $\sqrt{x(1-x)} = \sqrt{x} \sqrt{1-x}$.So, $I = \int \frac{dx}{\sqrt{x} \s

Vedclass · Accepted Answer

$2 \sin^{-1} \sqrt{x} + C$

Vedclass · Answer

(A) Let $I = \int \frac{dx}{\sqrt{x-x^2}}$.We can rewrite the denominator as $\sqrt{x(1-x)} = \sqrt{x} \sqrt{1-x}$.So, $I = \int \frac{dx}{\sqrt{x} \sqrt{1-x}}$.Let $\sqrt{x} = \sin 	heta$. Then $x = \sin^2 	heta$, which implies $dx = 2 \sin 	heta \cos 	heta \, d	heta$.Substituting these into the integral:$I = \int \frac{2 \sin 	heta \cos 	heta \, d	heta}{\sin 	heta \sqrt{1-\sin^2 	heta}}$$I = \int \frac{2 \sin 	heta \cos 	heta \, d	heta}{\sin 	heta \cos 	heta}$$I = \int 2 \, d	heta = 2	heta + C$.Since $\sin 	heta = \sqrt{x}$, we have $	heta = \sin^{-1} \sqrt{x}$.Therefore, $I = 2 \sin^{-1} \sqrt{x} + C$.

$\int \frac{dx}{\sqrt{x-x^2}}$ is equal to

Similar Questions

If $f(x) = (x^2 - 1)^7$,then $f^{(14)}(x)$ is equal to

The length of the common chord of the two circles $x^2+y^2-4y=0$ and $x^2+y^2-8x-4y+11=0$ is

The part of the castor seed from which oil is obtained is called the .....

When phenyl magnesium bromide reacts with $t-$butanol,the product would be

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

Vedclass Test Series

Exam Paper Generator

Online Exam Module