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1.11 H: Integration

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Question 149

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.

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Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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