Question

But for all arbitrary constants, $\smallint \,\,\sqrt {\frac{{1\,\, + \,\,\sin \,\,	heta \,\, - \,\,{{\sin }^2}\,\,	heta \,\, - \,\,{{\sin }^3}\,\,	heta }}{{2\,\,\sin \,\,	heta \,\, - \,\,1}}\,\,} d	heta \,\,{m{is }}\,{m{equal }}\,{m{to}}$

Accepted Answer

$\frac{1}{2}\,\,\sqrt {\sin \,\,	heta \,\, - \,\,\cos \,\,2\,	heta } \,\, + \,\,\frac{3}{{4\,\,\sqrt 2 }}\,\,{\log _e}\left| {\,\left( {4\,\,\sin \,\,	heta \,\, + \,\,1} ight)\,\, + \,\,2\,\,\sqrt 2 \,\,\sqrt {\sin \,\,	heta \,\, - \,\,\cos \,\,2\,\

Answer

$\frac{1}{2}\,\,\sqrt {\sin \,\,	heta \,\, + \,\,\cos \,\,2\,	heta } \,\, + \,\,\frac{3}{{4\,\,\sqrt 2 }}\,\,{\log _e}\,\,\left| {\,\left( {4\,\,\sin \,\,	heta \,\, - \,\,1} ight)\,\, + \,\,2\,\,\sqrt 2 \,\,\sqrt {\sin \,\,	heta \,\, + \,\,\cos \,\,

Answer

$\frac{1}{{2\,\,\sqrt 2 }}\,\,\sqrt {\sin \,\,	heta \,\, - \,\,\cos \,\,2	heta } \,\, + \,\,\frac{3}{4}\,\,{\log _e}\,\,\left| {\,\left( {4\,\,\sin \,\,	heta \,\, + \,\,1} ight)\,\, - \,\,\sqrt {\sin \,\,	heta \,\, - \,\,\cos \,\,2\,\,	heta } \,} \

Answer

$\frac{1}{2}\,\,\sqrt {\,\,\sin \,\,	heta \,\, + \,\,\cos \,\,2\,	heta } \,\, + \,\,\frac{3}{{4\,\,\sqrt 2 }}\,\,{\log _e}\,\,\left| {\,4\,\,\sin \,\,	heta \,\, + \,\,1\,\, - \,\,\sqrt {\sin \,\,	heta \,\, - \,\,\cos \,\,2\,\,	heta \,} } ight|$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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