Výpočet určitého integrálu
Urči hodnoty určitého integrálu pomocí substituce:
\large{\displaystyle\int\limits_{\Large\frac{\pi}{4}}^{\pi}\Large\frac{\sin{4x}}{2}{d}x}
\large \Large \frac{1}{8}\large \left[ -\cos {u} \right] ^{4\pi}_{\pi} = \Large \frac{1}{8}\large \left[ \left( -\cos {4 \pi}\right) -\left( -\cos {\pi}\right) \right] = \Large \frac{1}{8}\large \cdot \left( -1+1\right) =0
\large \Large \frac{1}{8}\large \left[ -\cos {u} \right] ^{4\pi}_{\pi} = \Large \frac{1}{8}\large \left[ \left( -\cos {4 \pi}\right) -\left( -\cos {\pi}\right) \right] = \Large \frac{1}{8}\large \cdot \left( 1+1\right) =\Large \frac{1}{4}\large
\large \Large \frac{1}{8}\large \left[ -\cos {u} \right] ^{4\pi}_{\pi} = \Large \frac{1}{8}\large \left[ \left( -\cos {4 \pi}\right) -\left( -\cos {\pi}\right) \right] = \Large \frac{1}{8}\large \cdot \left( 1-1\right) =0
\large \Large \frac{1}{8}\large \left[ -\cos {u} \right] ^{4\pi}_{\pi} = \Large \frac{1}{8}\large \left[ \left( -\cos {4 \pi}\right) -\left( -\cos {\pi}\right) \right] = \Large \frac{1}{8}\large \cdot \left( -1-1\right) =-\Large \frac{1}{4}\large