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

$\frac{a}{b}\,\,{\tan ^{ - 1}}\,\,\left( {\frac{{a\,\,\tan \,\,x}}{b}} \right)\,\, + \,\,c$

$\frac{b}{a}\,\,{\tan ^{ - 1}}\,\,\left( {\frac{{b\,\,\tan \,\,x}}{b}} \right)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{dx}}{{{a^2}\,\,{{\sin }^2}\,\,x\,\, + \,\,{b^2}\,\,{{\cos }^2}\,\,x}}

is equal to

View answer and explanation

Correct option: A

\frac{1}{{ab}}\,\,{\tan ^{ - 1}}\,\,\left( {\frac{{a\,\,\tan \,\,x}}{b}} \right)\,\, + \,\,c

Option A (

\frac{1}{{ab}}\,{\tan ^{ - 1}}\,\,\left( {\frac{{a\,\,\tan \,\,x}}{b}} \right)\,\, + \,\,c

) is correct because the integral can be solved by dividing by cos²(x) and using a suitable substitution.