If int frac{d x}{sqrt{sin ^3 x cos x}}=g(x)+c | vedclass

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

Question

(B) Given, $I = \int \frac{d x}{\sqrt{\sin ^3 x \cos x}}$.We can rewrite the integrand as:$I = \int \frac{d x}{\sqrt{\sin ^4 x \cdot \frac{\cos x}{\si

Vedclass · Accepted Answer

$\frac{-2}{\sqrt{	an x}}$

Vedclass · Answer

(B) Given, $I = \int \frac{d x}{\sqrt{\sin ^3 x \cos x}}$.We can rewrite the integrand as:$I = \int \frac{d x}{\sqrt{\sin ^4 x \cdot \frac{\cos x}{\sin x}}} = \int \frac{d x}{\sin ^2 x \sqrt{\cot x}}$.Since $\frac{1}{\sin ^2 x} = \operatorname{cosec}^2 x$, we have:$I = \int \frac{\operatorname{cosec}^2 x}{\sqrt{\cot x}} d x$.Let $t = \cot x$. Then $dt = -\operatorname{cosec}^2 x d x$, which implies $\operatorname{cosec}^2 x d x = -dt$.Substituting these into the integral:$I = \int \frac{-dt}{\sqrt{t}} = -\int t^{-1/2} dt$.Integrating with respect to $t$:$I = -\frac{t^{1/2}}{1/2} + c = -2\sqrt{t} + c$.Substituting $t = \cot x$ back:$I = -2\sqrt{\cot x} + c = -\frac{2}{\sqrt{	an x}} + c$.Comparing this with $g(x) + c$, we get $g(x) = -\frac{2}{\sqrt{	an x}}$.

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$, then $g(x)$ is equal to

Similar Questions

Statement $P$: Every living organism exhibits unique characteristics such as reproduction,growth,development,adaptation,and death.
Statement $Q$: Energy transformation is essential for every living organism.

The longest distance of the point $(a, 0)$ from the curve $2 x^2+y^2=2 x$ is

If the circle $x^2+y^2+6x-2y+k=0$ bisects the circumference of the circle $x^2+y^2+2x-6y-15=0$,then $k=$

Total emf produced in a thermocouple does not depend on

Decomposers are

Vedclass Test Series

Exam Paper Generator

Online Exam Module