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Question 452

The rate at which a submersible drone consumes battery power, P(t)P(t)P(t) in watts, is modeled by the function:

P(t)=20t3−65t4+92 P(t) = 20t^3 - \frac{6}{5t^4} + \frac{9}{2} P(t)=20t3−5t46​+29​

where t>0t > 0t>0 is the duration of the mission in hours. Find an expression for the total energy consumption by evaluating the indefinite integral:

∫(20t3−65t4+92)dt \int \left( 20t^3 - \frac{6}{5t^4} + \frac{9}{2} \right) dt ∫(20t3−5t46​+29​)dt

giving each term in its simplest form.

[4]
Markscheme

Integration Questions

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

787 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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