Evaluate, <p></p> $\int {\left\{ {{{\left( {\frac{x}{e}} \right)}^x} + {{\left( {\frac{e}{x}} \right)}^x}} \right\}} \ln xdx$

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Evaluate,
$\int {\left\{ {{{\left( {\frac{x}{e}} \right)}^x} + {{\left( {\frac{e}{x}} \right)}^x}} \right\}} \ln xdx$

Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $ $\therefore 2^n = 4096 =2^{12} $ $\Rightarrow n = 12 $ Greatest coefficient = ${}^{12}{C_6} = 924$

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Evaluate,
$\int {\left\{ {{{\left( {\frac{x}{e}} \right)}^x} + {{\left( {\frac{e}{x}} \right)}^x}} \right\}} \ln xdx$

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Sum of the coefficients in the expansion of $(x+y)^n$ ....

123IITJEE

Evaluate, $\int {\left\{ {{{\left( {\frac{x}{e}} \right)}^x} + {{\left( {\frac{e}{x}} \right)}^x}} \right\}} \ln xdx$

Popular posts from this blog

Sum of the coefficients in the expansion of $(x+y)^n$ ....

Evaluate,
$\int {\left\{ {{{\left( {\frac{x}{e}} \right)}^x} + {{\left( {\frac{e}{x}} \right)}^x}} \right\}} \ln xdx$