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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
