Mathematics

# If $f$ is continuous on $[0, 1]$ such that $f(x)+f\left(x+\dfrac{1}{2}\right)=1$ and $\displaystyle \int_{0}^{1}{f(x)dx}=k$, then value of $2K$ is

$1$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Medium
the value of the difinite $\int _{ 1 }^{ e }{ \left( \left( x+1 \right) { e }^{ x }lnx \right) dx\quad is- }$
• A. ${ e }^{ e+1 }$
• B. ${ e }^{ e }\left( e-1 \right)$
• C. ${ e }^{ e }\left( e-1 \right) +e$
• D. e

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate:

$\displaystyle\int {\dfrac{{{{\left( {x + a} \right)}^2}}}{{\sqrt x }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int { \cfrac { dx }{ \sqrt { 2{ e }^{ x }-1 } } }$ equals to
• A. $\sec ^{ -1 }{ \sqrt { 2{ e }^{ x } } } +c$
• B. $\sec ^{ -1 }{ \left( \sqrt { 2 } { e }^{ x } \right) } +c$
• C. $2\sec ^{ -1 }{ \left( \sqrt { 2 } { e }^{ x } \right) } +c$
• D. $2\sec ^{ -1 }{ \sqrt { 2{ e }^{ x } } } +c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle I= \int_{0}^{1}\frac{x dx}{8+x^{3}}$ then the smallest interval in which $I$ lies is
• A. $\displaystyle \left ( 0,\frac{1}{8} \right )$
• B. $\displaystyle \left ( 0,\frac{1}{10} \right )$
• C. $\displaystyle \left ( 0,\frac{1}{7} \right )$
• D. $\displaystyle \left ( 0,\frac{1}{9} \right )$

Evaluate: $\displaystyle\int {\frac{1}{{{a^x}{b^x}}}} \,dx$