Mathematics

Evaluate the following integrals$\int { \cfrac { 1 }{ 1-\tan { x } } } dx\quad$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

Realted Questions

Q1 Subjective Medium
Solve $\displaystyle\int\dfrac {\sqrt {\tan x}}{\sin x \cos x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int { \left( \cfrac { x-a }{ x } -\cfrac { x }{ x+a } \right) } dx$ is equal to
• A. $\log { \left| \cfrac { x+a }{ x } \right| } +C$
• B. $a\log { \left| \cfrac { x }{ x+a } \right| } +C$
• C. $\log { \left| \cfrac { x }{ x+a } \right| } +C$
• D. $a\log { \left| \cfrac { x-a }{ x+a } \right| } +C$
• E. $a\log { \left| \cfrac { x+a }{ x } \right| } +C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int^{\dfrac{\pi}{4}}_0\dfrac{x\sin x}{\cos^3x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\int ( \sin 2 x - \cos 2 x ) d x = \frac { 1 } { \sqrt { 2 } } \sin ( 2 x - a ) + C$ then
• A. $a = \frac { 5 \pi } { 4 } -2, C \in R$
• B. $a = \frac { \pi } { 4 } , C \in R$
• C. $a = \frac { \pi } { 2 } , C \in R$
• D. $a = \frac { 5 \pi } { 4 } , C \in R$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The function$int {:R \to \left[ { - \frac{1}{2},\frac{1}{2}} \right]}$ defined as
$\int {(x) = \frac{x}{{1 + x2}}}$ is ( 2017 main offline)
• A. surjective but not injective
• B. neither injective nor surjective
• C. invertible
• D. Injective but not Surjective