Mathematics

# If $\int _{ log2 }^{ x }{ \dfrac { dx }{ \sqrt { { e }^{ x }-1 } } } =\dfrac { \pi }{ 6 } ,$then x is equal to _________.

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

#### Realted Questions

Q1 Single Correct Hard
$\int \dfrac {x^{2}dx}{(x\sin x + \cos x)^{2}}$ is equal to
• A. $\dfrac {\sin x + \cos x}{x\sin x + \cos x}$
• B. $\dfrac {x\sin x - \cos x}{x\sin x + \cos x} + c$
• C. $\dfrac {\sin x - \cos x}{x\sin x + \cos x}x$
• D. None of these

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Find
$\displaystyle\int {\dfrac{{dt}}{{\sqrt t }}} + \left( {3 - \dfrac{4}{3}} \right)\displaystyle\int {\frac{{dx}}{{\sqrt {3{x^2} + 4x + 1} }}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral:
$\displaystyle\int_{0}^{\pi} x\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int_{}^{} {\dfrac{{{{\sec }^8}x}}{{\cos ecx}}dx} =$
• A. $\dfrac{{{{\cos }^7}x}}{7} + c$
• B. $\dfrac{7}{{{{\cos }^7}x}} + c$
• C. $\dfrac{1}{{{{\cos }^7}x}} + c$
• D. $\dfrac{1}{{7{{\cos }^7}x}} + c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
If $\displaystyle I= \int_{1/\pi }^{\pi }\frac{1}{x}\cdot \sin \left ( x-\frac{1}{x} \right )dx$ then I is equal to
• A. $\displaystyle \pi$
• B. $\displaystyle \pi -\frac{1}{\pi }$
• C. $\displaystyle \pi +\frac{1}{\pi }$
• D. $0$