Mathematics

# If $f(x)=\int_{0}^{x}t (sinx - sint)dt$  then:

$f'''(x)+f'(x)= cosx - 2x sinx$

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

#### Realted Questions

Q1 Subjective Medium
Integrate the following:
$\displaystyle \int\limits_{\pi /3}^{\pi /2} {{{(\tan x + \cot x)}^2}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Hard
If $\displaystyle \int_{0}^{\pi}\frac{x^{2}\cos x}{(1+\sin x)^{2}}dx=A \pi-\pi^{2}$ then A is

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int { \dfrac { \sqrt { 4+{ x }^{ 2 } } }{ { x }^{ 6 } } dx } =\dfrac { { \left( a+{ x }^{ 2 } \right) }^{ 3/2 }\left( { x }^{ 2 }-b \right) }{ 120{ x }^{ 5 } }+C$ then $a+b$ equals to:

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int \frac{\sec^{2}x dx}{\sqrt{\tan^{2} x+4}}=$
• A. $\dfrac{1}{2}\ln\left ( \tan x+\sqrt{\tan^{2} x+4} \right )+C$
• B. $\ln\left ( \dfrac{1}{2}\tan x+\dfrac{1}{2}\sqrt{\tan^{2} x+4} \right )+C$
• C. None of these
• D. $\ln\left ( \tan x+\sqrt{\tan^{2} x+4} \right )+C$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
$\int { \cfrac { \cos { x } }{ \left( 1+\sin ^{ 2 }{ x } \right) } } dx=$?
• A. $-\tan ^{ -1 }{ \left( \sin { x } \right) } +C$
• B. $\tan ^{ -1 }{ \left( \cos { x } \right) } +C$
• C. $-\tan ^{ -1 }{ \left( \cos { x } \right) } +C$
• D. $\tan ^{ -1 }{ \left( \sin { x } \right) } +C$