jee-main 2017 Q82

jee-main · India · 08apr Standard Integrals and Reverse Chain Rule Definite Integral Evaluation via Substitution or Standard Forms

The integral $\int \sqrt { 1 + 2 \cot x ( \operatorname { cosec } x + \cot x ) } d x , \left( 0 < x < \frac { \pi } { 2 } \right)$ is equal to
(1) $2 \log \left| \sin \frac { x } { 2 } \right| + c$
(2) $4 \log \left| \sin \frac { x } { 2 } \right| + c$
(3) $4 \log \left| \cos \frac { x } { 2 } \right| + c$
(4) $2 \log \left| \cos \frac { x } { 2 } \right| + c$

The integral $\int \sqrt { 1 + 2 \cot x ( \operatorname { cosec } x + \cot x ) } d x , \left( 0 < x < \frac { \pi } { 2 } \right)$ is equal to\\
(1) $2 \log \left| \sin \frac { x } { 2 } \right| + c$\\
(2) $4 \log \left| \sin \frac { x } { 2 } \right| + c$\\
(3) $4 \log \left| \cos \frac { x } { 2 } \right| + c$\\
(4) $2 \log \left| \cos \frac { x } { 2 } \right| + c$

Paper Questions

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