Mathematics

# $\displaystyle\int^{\dfrac{\pi}{4}}_{\dfrac{-\pi}{4}}\sqrt{\dfrac{1-\cos 2008x}{2}}dx$ equals?

$\dfrac{1}{249}$

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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
Prove that $\displaystyle\int^{\pi/2}_0(\sin x-\cos x)log (\sin x+\cos x)dx=0$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
a) Prove that $\displaystyle \overset {a}{ \underset {a}{\int}}f(x)dx=\begin{cases}2\overset { a }{ \underset { 0 }{\displaystyle \int } } f(x)dx & \text{if }f (x) \text{ is an even function} \\ 0 & \text{if }f (x)\text{ is an odd function} \end{cases}$
and hence evaluate $\displaystyle\overset { 1 }{ \underset { -1 }{\int} } {\sin}^5 x {\cos}^4 x dx$.
b) Prove that
$\begin{vmatrix}a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ca & cb & c^2+1\end{vmatrix} = 1+a^2+b^2+c^2$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate
$\displaystyle\int \frac { \sec ^ { 2 } \sqrt { x } } { \sqrt { x } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle 4\int \frac{a^{6}+x^{8}}{x}dx$ is equal to
• A. $4a^6 \log a+\dfrac{x^8}{8}+C$
• B. $a^6 \log x+\dfrac{x^8}{8}+C$
• C. $4a^6 \log x+\dfrac{x^8}{8}+C$
• D. $4a^6 \log x+\dfrac{x^8}{2}+C$

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.