Mathematics

# The integral $\displaystyle \int_{\dfrac{\pi}{12}}^{\dfrac{\pi}{4}}{\dfrac{8\cos 2x}{(\tan x+\cot x)^{3}}dx}$ equals :

$\dfrac{15}{128}$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
The integral $\displaystyle\int { \dfrac { x+2 }{ \left( { x }^{ 2 }+3x+3 \right) \sqrt { x+1 } } } dx$ is equal to
• A. $\dfrac { 2 }{ \sqrt { 3 } } \tan ^{ -1 }{ \left[ -\dfrac { x }{ \sqrt { 3\left( x+1 \right) } } \right] } +C$
• B. $\dfrac { 2 }{ \sqrt { 3 } } \cot ^{ -1 }{ \left[ -\dfrac { x }{ \sqrt { \left( x+1 \right) } } \right] } +C$
• C. $\dfrac { 1 }{ \sqrt { 3 } } \cot ^{ -1 }{ \left[ -\dfrac { x\sqrt { 3 } }{ \sqrt { x+1 } } \right] } +C$
• D. $\dfrac { 1 }{ \sqrt { 3 } } \tan ^{ -1 }{ \left[ -\dfrac { x }{ \sqrt { 3\left( x+1 \right) } } \right] } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $l_{n}=\displaystyle \int{\dfrac{t^{n}}{1+t^{2}}}dt$ then
• A. $l_{n+1}=\dfrac{t^{n+1}}{n+1}l_{n}$
• B. $l_{n+1}=\dfrac{t^{n-1}}{n-1}l_{n}$
• C. $l_{n21}=\dfrac{t^{n+1}}{n+1}l_{n}$
• D. $l_{n+2}=\dfrac{t^{n}}{n}-nl_{n}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\displaystyle \int e^{\sin x}\sin 2xdx$
• A. $2e^{\sin x}(\sin x+1)+c$
• B. $e^{\sin x}(\sin x+2)+c$
• C. $e^{\sin x}(3\sin x -2)+c$
• D. $e^{\sin x}(2\sin x-2)+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate :
$\int { { sin }^{ 2 }x } dx$

If $y=2^23^{2x}5^{-5}7^{-5}$ then $\dfrac{dy}{dx}=$