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Mathematics

This Exam is on Definite Integral for Class 12th and Repeater Students

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Q:1. If \int _{ 0 }^{ \frac { \pi }{ 3 } }{ \frac { \cos { x } }{ 3+4\sin { x } } } dx\quad =\quad k\quad \ln { \left( \frac { 2+2\sqrt { 3 } }{ 3 } \right) , } then\quad k\quad =

(a)\frac { 1 }{ 2 }    (b)\frac { 1 }{ 3 }   (c) \frac { 1 }{ 4 }  (d) \frac { 1 }{ 8 }

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Q:2. \int _{ 0 }^{ \frac { \pi }{ 4 } }{ \frac { \sin { x } +\cos { x } }{ 9+16\sin { 2x } } } dx=

(a) \frac { \ln { 2 } }{ 20 }  (b) \frac { \ln { 2 } }{ 10 }  (c) \frac { \ln { 3 } }{ 20 }  (d) \frac { \ln { 3 } }{ 10 }

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Q:3. \int _{ 0 }^{ 1 }{ \left( 1+{ e }^{ { -x }^{ 2 } } \right) } dx=

(a) -1   (b) 2  (c) 1+{ e }^{ -1 }  (d) None of these