|
|
|
|
|
|
|
|
|
|
Cho $I = \int\limits_{0}^{1} {{e^{ - \frac{{{x^2}}}{2}}}dx = 0,34.\sqrt {2 \times 3,14} } $
Tính $K = \frac{1}{{a\sqrt {2 \times 3,14} }}.\int\limits_{b - a}^{b + a} {{e^{\frac{{ - {{\left( {x - b} \right)}^2}}}{{2{a^2}}}}}dx} \,\,\,\,\,\,\,\,\,\,\,\,(a,b > 0)$
|
Tính :
$\begin{array}{l}
1)\,\,\,\,\,I = \,\,\,\int\limits_0^{\frac{1}{2}} {\frac{{{x^4}}}{{{x^2} - 1}}dx} \\
2)\,\,\,\,{I_{\left( t \right)}} = \int\limits_0^t {\frac{{tan^{4}xdx}}{{cos\,2x}}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(0 < t < \frac{\pi }{4})
\end{array}$
Và chứng minh bất đẳng thức :
$tan\left( {t + \frac{\pi }{4}} \right) > {e^{\frac{2}{3}\left( {tan{^3}t + 3tant} \right)}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 < t < \frac{\pi }{4}$
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|