Mathematics

# $\displaystyle\int^{2\pi}_0[\sin x]dx$.

$\pi$

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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 Medium
Evaluate:
$\displaystyle\int{\dfrac{{x}^{2}}{1+{x}^{3}}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\displaystyle \int\dfrac{\sin x}{\sin (x-a)}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int { \dfrac { \left( x+2 \right) dx }{ \sqrt { \left( x-2 \right) \left( x-3 \right) } } }$ is equal to:
• A. $\sqrt{x^2-5x+6}-\frac{9}{2}\log\left(x-\frac{5}{2}\right)+\sqrt{x^2-5x+6}$
• B. $\sqrt{x^2-5x+6}-\frac{9}{2}\log\left(x-\frac{5}{2}\right)-\sqrt{x^2-5x+6}$
• C. $\sqrt{x^2-5x+6}+\frac{9}{2}\log\left(x-\frac{5}{2}\right)-\sqrt{x^2-5x+6}$
• D. $\sqrt{x^2-5x+6}+\frac{9}{2}\log\left(x-\frac{5}{2}\right)+\sqrt{x^2-5x+6}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The integral $\displaystyle \int _{ \frac { x }{ 12 } }^{ \frac { x }{ 4 } }{ \frac { 8\cos { 2x } }{ { \left( \tan { x } +\cot { x } \right) }^{ 3 } } dx }$ is equal to
• A. $\dfrac {5}{128}$
• B. $\dfrac {15}{64}$
• C. $\dfrac {13}{256}$
• D. $\dfrac {13}{32}$

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.