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Question 433

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

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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