int frac{sin ^{-1} x}{sqrt{1-x^2}} d x is equ | vedclass

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

Question

(B) To evaluate the integral $I = \int \frac{\sin ^{-1} x}{\sqrt{1-x^2}} d x$,we use the method of substitution.Let $t = \sin ^{-1} x$.Then,differenti

Vedclass · Accepted Answer

$\frac{1}{2}\left(\sin ^{-1} x\right)^2+c$

Vedclass · Answer

(B) To evaluate the integral $I = \int \frac{\sin ^{-1} x}{\sqrt{1-x^2}} d x$,we use the method of substitution.Let $t = \sin ^{-1} x$.Then,differentiating both sides with respect to $x$,we get $\frac{dt}{dx} = \frac{1}{\sqrt{1-x^2}}$,which implies $dt = \frac{1}{\sqrt{1-x^2}} dx$.Substituting these into the integral,we get $I = \int t dt$.Integrating with respect to $t$,we obtain $I = \frac{1}{2} t^2 + c$.Finally,substituting $t = \sin ^{-1} x$ back into the expression,we get $I = \frac{1}{2} (\sin ^{-1} x)^2 + c$.

$\int \frac{\sin ^{-1} x}{\sqrt{1-x^2}} d x$ is equal to,where $c$ is an arbitrary constant.

Similar Questions

$\int \frac{d x}{x\left(x^4+1\right)}=$

Integrate the function $\frac{1}{x(\log x)^{m}}$,where $x > 0$ and $m \neq 1$.

$\int \sin ^3(x) \cdot \cos ^3(x) \, dx =$

$\int \sec^{2/3} x \csc^{4/3} x \, dx = $

Find the following integral: $\int \frac{dx}{\sqrt{2x-x^2}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module