int frac{dx}{a^2 sin^2 x + b^2 cos^2 x} is eq | vedclass

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

Question

(A) To evaluate the integral $I = \int \frac{dx}{a^2 \sin^2 x + b^2 \cos^2 x}$,divide the numerator and denominator by $\cos^2 x$:$I = \int \frac{\sec

Vedclass · Accepted Answer

$\frac{1}{ab} 	an^{-1}\left(\frac{a 	an x}{b}ight) + C$

Vedclass · Answer

(A) To evaluate the integral $I = \int \frac{dx}{a^2 \sin^2 x + b^2 \cos^2 x}$,divide the numerator and denominator by $\cos^2 x$:$I = \int \frac{\sec^2 x dx}{a^2 	an^2 x + b^2}$Now,let $u = 	an x$,then $du = \sec^2 x dx$:$I = \int \frac{du}{a^2 u^2 + b^2} = \frac{1}{a^2} \int \frac{du}{u^2 + (b/a)^2}$Using the standard integral formula $\int \frac{dx}{x^2 + k^2} = \frac{1}{k} 	an^{-1}\left(\frac{x}{k}ight) + C$:$I = \frac{1}{a^2} \cdot \frac{1}{b/a} 	an^{-1}\left(\frac{u}{b/a}ight) + C$$I = \frac{1}{ab} 	an^{-1}\left(\frac{a 	an x}{b}ight) + C$

$\int \frac{dx}{a^2 \sin^2 x + b^2 \cos^2 x}$ is equal to

Similar Questions

The electric field associated with an $e.m.$ wave in vacuum is given by $\vec E = \hat i\,40\,\cos \left( {kz - 6 \times {{10}^8}\,t} \right)$,where $E$,$z$,and $t$ are in $V/m$,$m$,and $s$ respectively. The value of the wave vector $k$ is ....... $m^{-1}$.

Which of the following is an incorrect statement?

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

If $2 x^2-3 x y+y^2+x+2 y-8=0$, then $\frac{d y}{d x}$ is equal to

The major product of the following reaction is

Vedclass Test Series

Exam Paper Generator

Online Exam Module