Mathematics

$\int _{ 0 }^{ \pi /3 }{ \dfrac { \tan { \theta } }{ \sqrt { 2k\sec { \theta } } } } d\theta =1-\dfrac { 1 }{ \sqrt { 2 } }$. Then $k$ is-

$3$

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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
$\displaystyle \int_1^{32}\dfrac{dx}{x^{1/5}\sqrt{1+x^{4/5}}}$
• A. $\dfrac{2}{5}(\sqrt{17}-\sqrt{2})$
• B. $\dfrac{5}{2}(\sqrt{17}-\sqrt{2})$
• C. $\dfrac{5}{2}(\sqrt{17}+\sqrt{2})$
• D. $\dfrac{2}{5}(\sqrt{17}+\sqrt{2})$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { \cfrac { 5x+3 }{ \sqrt { { x }^{ 2 }+4x+10 } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle\int_{0}^{1}\dfrac{2x}{1+x^{4}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Let $\displaystyle f\left ( x \right )=\int_{0}^{x}t\sin tdt$, then $\displaystyle f\left ( x \right )$ is equal to
• A. $\displaystyle \cos x+x\sin x.$
• B. $\displaystyle x \cos x.$
• C. None of these
• D. $\sin x-x\cos x$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
The value of $\displaystyle \int { \dfrac { \cos { 5x } +\cos { 4x } }{ 1-2\cos { 3x } } dx }$, is equal to
• A. $\sin{x}+\sin{2x}+c$
• B. $\sin{x}-\dfrac{\sin{2x}}{2}+c$
• C. $-\sin{x}-\dfrac{\sin{2x}}{2}+c$
• D. $\sin{x}+\dfrac{1}{2}\sin{2x}+c$