Mathematics

# Find m if :$\displaystyle \int_{0}^{\pi}\left ( \dfrac{\sqrt{1+\cos\ 2x}}{2} \right )dx=\sqrt m$

##### SOLUTION
$\displaystyle\int_{0}^{\pi}{\left(\dfrac{\sqrt{1+\cos{2x}}}{2}\right)dx}$
$=\displaystyle\int_{0}^{\pi}{\left(\dfrac{\sqrt{1+2{\cos}^{2}{x}-1}}{2}\right)dx}$
$=\dfrac{\sqrt{2}}{2}\displaystyle\int_{0}^{\pi}{\cos{x}dx}$
$=\dfrac{\sqrt{2}}{2}\left[\sin{x}\right]_{0}^{\pi}$
$=\dfrac{\sqrt{2}}{2}\left[\sin{\pi}-\sin{0}\right]=0$
$\therefore\,m=0$

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One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

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$\int { \cfrac { 3{ x }^{ 5 } }{ \left( 1+{ x }^{ 12 } \right) } } dx=$?
• A. $\tan ^{ -1 }{ { x }^{ 6 } } +C$
• B. $\cfrac { 1 }{ 4 } \tan ^{ -1 }{ { x }^{ 6 } } +C$
• C. none of these
• D. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ { x }^{ 6 } } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\int { \dfrac { \sqrt { 4+{ x }^{ 2 } } }{ { x }^{ 6 } } dx } =\dfrac { { \left( a+{ x }^{ 2 } \right) }^{ 3/2 }\left( { x }^{ 2 }-b \right) }{ 120{ x }^{ 5 } }+C$ then $a+b$ equals to:

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate $\displaystyle\int{\sqrt{x+\sqrt{x^2+2}}dx}$.
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1 Verified Answer | Published on 17th 09, 2020

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1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
If $y=\displaystyle\int \dfrac {dx}{(1+x^{2})^{\frac {1}{2}}}$ and $y=0$ when $x=0$, then value of $y$ when$x=1$, is:
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