Section 1
Test exercise F.19
Find the area bounded by the curves $y=3 e^{2 x}$ and $y=3 e^{-x}$ and the ordinates at $x=1$ and $x=2$.
The parametric equations of a curve are$$y=2 \sin \frac{\pi}{10} t, \quad x=2+2 t-2 \cos \frac{\pi}{10} t.$$Find the area under the curve between $t=0$ and $t=10$.
Find the mean value of $y=\frac{5}{2-x-3 x^{2}}$ between $x=-\frac{1}{3}$ and $x=+\frac{1}{3}$.
Calculate the rms value of $i=20+100 \sin 100 \pi t$ between $t=0$ and $t=1 / 50$.
If $i=I \sin \omega t$ and $v=L \frac{\mathrm{d} i}{\mathrm{~d} t}+R i$, find the mean value of the product $v i$ between $t=0$ and $t=\frac{2 \pi}{\omega}$.
If $i=300 \sin 100 \pi t+I$, and the rms value of $i$ between $t=0$ and $t=0.02$ is 250, determine the value of $I$.