jee-main 2016 Q83

jee-main · India · 10apr Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression)

The integral $\int \frac { d x } { ( 1 + \sqrt { x } ) \sqrt { x - x ^ { 2 } } }$ is equal to
(1) $- 2 \sqrt { \frac { 1 + \sqrt { x } } { 1 - \sqrt { x } } } + c$
(2) $- \sqrt { \frac { 1 - \sqrt { x } } { 1 + \sqrt { x } } } + c$
(3) $- 2 \sqrt { \frac { 1 - \sqrt { x } } { 1 + \sqrt { x } } } + c$
(4) $\sqrt { \frac { 1 + \sqrt { x } } { 1 - \sqrt { x } } } + c$

The integral $\int \frac { d x } { ( 1 + \sqrt { x } ) \sqrt { x - x ^ { 2 } } }$ is equal to\\
(1) $- 2 \sqrt { \frac { 1 + \sqrt { x } } { 1 - \sqrt { x } } } + c$\\
(2) $- \sqrt { \frac { 1 - \sqrt { x } } { 1 + \sqrt { x } } } + c$\\
(3) $- 2 \sqrt { \frac { 1 - \sqrt { x } } { 1 + \sqrt { x } } } + c$\\
(4) $\sqrt { \frac { 1 + \sqrt { x } } { 1 - \sqrt { x } } } + c$

Paper Questions

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