Mathematics

# $\displaystyle \int_{\pi/4}^{\pi/4} ln \sqrt{1+\sin2x}dx$ dx has the value equal to:

$\dfrac{\pi}{4}\ln2$

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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

If $f(x)=\displaystyle \frac{e^{x}}{1+e^{x}}$ ,$I_{1}=\displaystyle \int_{f(-a)}^{f(a)}xg\{x(1-x)\}dx$ and $I_{2}=\displaystyle \int_{f(-a)}^{f(a)}g\{x(1-x)\}dx$, then the value $\displaystyle \frac{I_{2}}{I_{1}}$ is
• A. -3
• B. -1
• C. 1
• D. 2

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Integrate
$\int {\frac{{2\sin 2x - \cos x}}{{6 - {{\cos }^2}x - 4{\mathop{\rm sinx}\nolimits} }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int \cos(\ln x)dx=$
• A. $\dfrac{x}{2}[\cos \ln x-\sin \ln x]$
• B. $[x \cos \ln x + \sin \ln x]$
• C. None of these
• D. $\dfrac{x}{2}(\cos \ln x+\sin \ln x)$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle \int_{1}^{x}\dfrac{dt}{|t|\sqrt{t^{2}-1}}=\dfrac{\pi}{6}$, then $x$ can be equal to :
• A. $\sqrt{3}$
• B. $2$
• C. $\dfrac{4}{\sqrt{3}}$
• D. $\dfrac{2}{\sqrt{3}}$

$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$