Mathematics

# Integrate with respect to x:$\sec^2 x\tan x$.

$\dfrac{tan^2x}{2}+C$

##### SOLUTION

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

#### Realted Questions

Q1 Single Correct Medium
The value of integral $\displaystyle \int _{ \pi /4 }^{ 3\pi /4 }{ \frac { x }{ 1+\sin x } dx }$ is
• A. $\pi \sqrt { 2 }$
• B. $\dfrac { \pi }{ 2 } (\sqrt { 2 } +1)$
• C. $2\pi (\sqrt { 2 } -1)$
• D. $\pi (\sqrt { 2 } -1)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Let $f$ be a positive function. Let
${ I }_{ 1 }=\int _{ 1-k }^{ k }{ xf\left\{ x(1-x) \right\} } dx$
${ I }_{ 2 }=\int _{ 1-k }^{ k }{ f\left\{ x(1-x) \right\} } dx$
where $2k-1>0$. Then $\cfrac { { I }_{ 1 } }{ { I }_{ 2 } }$
• A. $2$
• B. $k$
• C. $1$
• D. $\cfrac { 1 }{ 2 }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\int { { cosec }^{ 4 }x\ \ dx\quad }$
• A. $\cot { x+\dfrac { \cot ^{ 3 }{ x } }{ 3 } } +\quad c$
• B. $\tan { x +\dfrac { \tan ^{ 3 }{ x } }{ 3 } } +\quad c$
• C. $-\tan { x-\dfrac { \tan ^{ 3 }{ x } }{ 3 } } +\quad c$
• D. $-\cot { x- } \dfrac { \cot ^{ 3 }{ x } }{ 3 } +c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle\int\dfrac{4e^{x}+6e^{-x}}{9e^{x}-4e^{-x}}dx=Ax+B \log |9e^{2x}-4|+c$, then $(A,B)=$
• A. $\left(\dfrac{-19}{36},\dfrac{35}{36}\right)$
• B. $\left(\dfrac{19}{36},\dfrac{-35}{36}\right)$
• C. $\left(\dfrac{3}{2},\dfrac{-35}{36}\right)$
• D. $\left(\dfrac{-3}{2},\dfrac{35}{36}\right)$

Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$