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Question 670

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)412t3​

where 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=∫02​P(t)dt, is exactly 527\frac{5}{27}275​ units.

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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