Mathematics

# $\int _{0}^{-\pi/2} \ln (\sin^{2}{\theta}+k^{2}\cos^{2}{\theta})d\theta$ is equal to

$\pi \ \ln ({\dfrac{k+1}{2}})$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Medium
Evaluate: $\displaystyle \int_{\sqrt{8}}^{\sqrt{15}}x\sqrt{1+x^{2}}.dx$
• A. $\dfrac{15}{8}$
• B. $\dfrac{37}{6}$
• C. $\displaystyle \frac{37}{9}$
• D. $\dfrac{37}{3}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate: $\displaystyle \int _{ \pi /4 }^{ \pi /2 }{ \cos { 2x } \log { \sin { x } } } dx$

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Q3 Single Correct Medium
Evaluate : $\displaystyle \int \frac{x^{3}+x+1}{x^{2}-1}dx$
• A. $\displaystyle =\frac{x^{3}}{2}+log\left | x^{3}-1 \right |+\frac{1}{2}log\left |\frac{x-1}{x+1} \right |+C$
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1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate: $\displaystyle\int \frac{x}{\sqrt{\left ( 1-x^{2} \right )}\cos ^{2}\sqrt{\left ( 1-x^{2} \right )}}dx$
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Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.
On the basis of above information answer the following questions

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020