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Tag Archives: Integration

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

March 4, 2014 Manish Verma Leave a comment

Evaluate,

Continue reading Evaluate \(\int {\left\{ {{{\left( {\frac{x}{e}} \right)}^x} + {{\left( {\frac{e}{x}} \right)}^x}} \right\}} \ln xdx\) →

JEE Advanced, Mathematics

Area Between y = sin x + cos x and y = |cos x – sin x|

February 28, 2014 Manish Verma Leave a comment

Only one option is correct.

[JEE Advanced 2013]

Continue reading Area Between y = sin x + cos x and y = |cos x – sin x| →

Area Integration

JEE Advanced, Mathematics

$\int\limits_{1/2}^1 {f(x)dx}$ lies in the interval

November 29, 2013 Manish Verma Leave a comment

Continue reading $\int\limits_{1/2}^1 {f(x)dx}$ lies in the interval →

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${\scriptscriptstyle 6 + f(x) = 2f( – x) + 3{x^2}\int\limits_{ – 1}^1 {f(t)dt}}$
$\scriptstyle f(x) = {\left( {\frac{x}{\pi }} \right)^x} + {\left( {\frac{\pi }{x}} \right)^x}$
$\scriptstyle \sqrt {7 – \sqrt {7 + \sqrt {7 – \sqrt {7 + …..} } } }$
$\scriptstyle f(x) = \int\limits_0^x {{\pi ^t}(t – e)(t – \pi )dt} $
$\scriptstyle 7f(x) + 5f\left( {\frac{1}{x}} \right) = x + 1$ …

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