Question

Помогите пожалуйста срочно !

Answer 1

Ответ:

$\displaystyle \int\limits^{e}_1\, \frac{1}{x}\, dx=ln|x|\Big|_1^{e}=lne-ln1=1-0=1\\\\\\\int\limits^{ln2}_0\, e^{x}\, dx=e^{x}\Big|_0^{ln2}=e^{ln2}-e^0=2-1=1\\\\\\\int\limits^{2\pi }_{-\pi }\, cosx\, dx=sinx\Big|_{-\pi }^{2\pi }=sin2\pi -sin(-\pi )=0-0=0\\\\\\\int\limits^{\pi }_{-2\pi }sinx\, dx=-cosx\Big|_{-2\pi }^{\pi }=-(cos\pi -cos(-2\pi ))=-(-1-1)=2$

$\displaystyle \int\limits^{\pi }_{-2\pi }\, sin2x\, dx=-\frac{1}{2}\cdot cos2x\Big|_{-2\pi }^{\pi }=-\frac{1}{2}\cdot (cos2\pi -cos(-4\pi ))=-\frac{1}{2}\cdot (1-1)=0\\\\\\ \int\limits^{0}_{-3\pi }\, cos3x\, dx=\frac{1}{3}\cdot sin3x\Big|_{-3\pi }^0=\frac{1}{3}\cdot (sin0-sin(-9\pi ))=\frac{1}{3}\cdot (0-0)=0$