int sqrt{operatorname{cosec} x - sin x} , dx | vedclass

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

Question

(A) Let $I = \int \sqrt{\operatorname{cosec} x - \sin x} \, dx$ $I = \int \sqrt{\frac{1}{\sin x} - \sin x} \, dx = \int \sqrt{\frac{1 - \sin^2 x}{\sin

Vedclass · Accepted Answer

$2 \sqrt{\sin x} + C$

Vedclass · Answer

(A) Let $I = \int \sqrt{\operatorname{cosec} x - \sin x} \, dx$ $I = \int \sqrt{\frac{1}{\sin x} - \sin x} \, dx = \int \sqrt{\frac{1 - \sin^2 x}{\sin x}} \, dx$ $I = \int \frac{\sqrt{\cos^2 x}}{\sqrt{\sin x}} \, dx = \int \frac{\cos x}{\sqrt{\sin x}} \, dx$ Let $u = \sin x$,then $du = \cos x \, dx$ $I = \int \frac{du}{\sqrt{u}} = \int u^{-1/2} \, du$ $I = \frac{u^{1/2}}{1/2} + C = 2\sqrt{u} + C$ Substituting $u = \sin x$,we get $I = 2\sqrt{\sin x} + C$

$\int \sqrt{\operatorname{cosec} x - \sin x} \, dx$ is equal to

Similar Questions

$\int \frac{1}{x^2 \sqrt{1-x^2}} \cdot d x = \dots + C$. Where,$(0 < |x| < 1)$.

$\int \cos ^3 x \cdot e^{\log (\sin x)} d x=$

If $\int \sin^{-1}\left(\sqrt{\frac{x}{a+x}}\right) dx = A(x) + \text{constant}$, then $A(x) =$

The integral $\int \frac{dx}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}$ is equal to (where $C$ is a constant of integration).

If $\int \frac{\sqrt{1-x^2}}{x^4} \,dx = A(x)\left(\sqrt{1-x^2}\right)^{m} + c$ for a suitably chosen integer $m$ and a function $A(x)$,where $c$ is a constant of integration,then $(A(x))^{m}$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module