Výpočet určitého integrálu
Urči hodnoty určitého integrálu pomocí substituce:
\large{\displaystyle\int\limits_0^1\Large\frac{x}{\sqrt{4-x^2}}{d}x}
\large \Large \frac{1}{2}\large \left[ 2 \sqrt {u} \right] ^4_3 = \Large \frac{1}{2}\large \left( 2 \sqrt {5}-2 \sqrt {3} \right) = \Large \frac{1}{2}\large \left( 4-2 \sqrt {3} \right) = 2-\sqrt {3}
\large \Large \frac{1}{2}\large \left[ 2 \sqrt {u} \right] ^4_3 = \Large \frac{1}{2}\large \left( 2 \sqrt {4}-2 \sqrt {3} \right) = \Large \frac{1}{2}\large \left( 4-2 \sqrt {3} \right) = 2-\sqrt {3}
\large \Large \frac{1}{2}\large \left[ 2 \sqrt {u} \right] ^4_3 = \Large \frac{1}{2}\large \left( 2 \sqrt {4}-2 \sqrt {2} \right) = \Large \frac{1}{2}\large \left( 4-2 \sqrt {2} \right) = 2-\sqrt {2}
\large \Large \frac{1}{2}\large \left[ 2 \sqrt {u} \right] ^4_3 = \Large \frac{1}{2}\large \left( 2 \sqrt {4}-2 \sqrt {3} \right) = \Large \frac{1}{2}\large \left( 4-2 \sqrt {4} \right) = 2-\sqrt {4}