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1.8 Integration

1.8 Integration

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Question 208

The instantaneous power output P(t)P(t)P(t) of a specific alternating current component, measured in Watts, is modeled by the function:

P(t)=(3sin⁡2t+5cos⁡2t)2 P(t) = (3\sin 2t + 5\cos 2t)^2 P(t)=(3sin2t+5cos2t)2

where ttt is the time in seconds. The total energy E(t)E(t)E(t) transferred by the component is given by E(t)=∫P(t) dtE(t) = \int P(t) \, dtE(t)=∫P(t)dt.

Determine the general expression for E(t)E(t)E(t) in its simplest form.

[6]
Markscheme

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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