Mathematics

# The integral $\int _{ \pi /4 }^{ \pi /2 }{ (2cosec\quad x)^{ 17 }dx }$ is equal to

$\int _{ 0 }^{ log(1+\sqrt { 2 } ) }{ 2{ (e }^{ u }+{ e }^{ -u }{ ) }^{ 16 }du }$

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

#### Realted Questions

Q1 Subjective Easy
Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Integrate the function:$\dfrac{1}{x+x\log{x}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle \int_{0}^{\pi }\displaystyle \frac{dx}{1-2\alpha \cos x+\alpha ^{2}}$ is
• A. $\displaystyle \frac{\pi }{1+\alpha ^{2}}$ if $\alpha > 1$
• B. $\displaystyle \frac{\pi }{1+\alpha ^{2}}$ if $\alpha < 1$
• C. $\displaystyle \frac{\pi }{\alpha ^{2}-1}$ if $\alpha < 1$
• D. $\displaystyle \frac{\pi }{\alpha ^{2}-1}$ if $\alpha > 1$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The integral $\displaystyle \int (1+x-\displaystyle \frac{1}{x})e^{x+\frac{1}{x}} dx$ is equal to
• A. $(x-1)e^{x+ \frac{1}{x}} +c$
• B. $(x+1)e^{x+\frac{1}{x}} +c$
• C. $-xe^{x+\frac{1}{x}} +c$
• D. $xe^{x+\frac{1}{x}} +c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Let $[\cdot]$ denote the greatest integer function then the value of $\displaystyle\int^{1.5}_0x[x^2]dx$ is?
• A. $0$
• B. $\dfrac{3}{2}$
• C. $\dfrac{5}{4}$
• D. $\dfrac{7}{4}$