Solve the problem.
-The voltage $\mathrm { v }$ (in volts) induced in a tape head is given by $\mathrm { v } = \mathrm { t } ^ { 2 } \mathrm { e } ^ { 3 \mathrm { t } }$, where $\mathrm { t }$ is the time (in seconds). Find the average value of $v$ over the interval from $t = 0$ to $t = 3$. Round to the nearest volt.
A) 1100 volts
B) 16 volts
C) 6502 volts
D) 71,327 volts

Question

Quizplus · Accepted Answer

The average value of a function $v(t)$ over an interval $[a, b]$ is given by $\frac{1}{b-a} \int_{a}^{b} v(t) \, dt$. For $v(t) = t^2 e^{3t}$ from $t = 0$ to $t = 3$, compute $\frac{1}{3-0} \int_{0}^{3} t^2 e^{3t} \, dt$. Solving this integral and rounding gives approximately 6502 volts.

Solve the Problem v\mathrm { v }v (In Volts) Induced in a Tape Head Is Given By Volts)

Solve the Problem $\mathrm { v }$ (In Volts) Induced in a Tape Head Is Given By Volts)