Mathematics

# The value of $\displaystyle \int _{0}^{\pi/2} \log{\sin{x}}dx$ is

$-\pi \log{2}$

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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 Medium
$\displaystyle\int _{ n }^{ n+1 }{ f(x) } dx=\begin{pmatrix} n \\ n-1 \end{pmatrix};n\in N$, then $\displaystyle\int _{ 1 }^{ 11 }{ f(x) } dx=$ _____
• A. $1023$
• B. $1024$
• C. $10$
• D. $55$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
For $\displaystyle x\in \,R$ let $f(x)=|\sin\,x|$ and $g(x)=\int^x_0\,f(t)dt.$ Let $p(x)=g(x)-\dfrac{2}{\pi}x$. Then
• A. $p(x+\pi)\neq p(x)$ for all least one but finitely many $x$
• B. $p(x+\pi)\neq p(x)$ for infinitely many $x$
• C. $p$ is a one-one function
• D. $p(x+\pi)=p(x)$ for all $x$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve
$\displaystyle \int{\dfrac{x}{(x^{2}+1)(x+1)}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find the integral of    $\displaystyle \int \left (\sqrt x-\frac {1}{\sqrt x}\right )^2dx$

$\int \frac{2x^{2}}{3x^{4}2x} dx$