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.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
