$\mathop \smallint \nolimits_0^\pi \,\,\,\,\frac{{x{\rm{ }}dx}}{{{a^2}\,\,{{\cos }^2}\,\,x\,\, + \,\,{b^2}\,\,{{\sin }^2}\,\,x}}\,\,{\rm{is }}\,{\rm{equal }}\,{\rm{to}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \nolimits_0^\pi \,\,\,\,\frac{{x\mathrm{ }dx}}{{{a^2}\,\,{{\cos }^2}\,\,x\,\, + \,\,{b^2}\,\,{{\sin }^2}\,\,x}}\,\,\mathrm{is }\,\mathrm{equal }\,\mathrm{to}

View answer and explanation

Correct option: C

\frac{{{\pi ^2}}}{{2\,ab}}

Option C (

\frac{{{\pi ^2}}}{{2\,ab}}

) is correct because the integral is solved using properties of definite integrals and trigonometric substitutions.

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