The power consumption PPP (in kilowatts) of a high-precision robotic arm during its activation phase is modeled by the function
P(t)=12t3(t2+2)4 P(t) = \frac{12t^3}{(t^2 + 2)^4} P(t)=(t2+2)412t3where ttt is the time in seconds for 0≤t≤20 \le t \le 20≤t≤2.
Use the substitution u=t2+2u = t^2 + 2u=t2+2 to show that the total energy EEE consumed by the arm during this 2-second phase, defined by E=∫02P(t) dtE = \int_{0}^{2} P(t) \, dtE=∫02P(t)dt, is exactly 527\frac{5}{27}275 units.
