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1.8 Integration

1.8 Integration

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Question 292

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]
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1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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