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Question 322
a.

Sketch the curve with equation

y=kx−7 y = k^x - 7 y=kx−7

where kkk is a constant such that k>1k > 1k>1.

On your sketch, show:

  • the coordinates of the point of intersection of the curve with the yyy-axis
  • the equation of the horizontal asymptote of the curve.
[3]
b.

The table below shows the power output PPP in kilowatts from a solar array, modeled by the equation P(t)=3t−1P(t) = 3^t - 1P(t)=3t−1, where ttt is the time in hours after dawn.

ttt00.511.52
PPP00.732124.19628

Using the trapezium rule with all the values of PPP in the given table, obtain an estimate for the total energy produced in the first two hours, given by

∫02(3t−1) dt \int_{0}^{2} (3^t - 1) \, dt ∫02​(3t−1)dt

giving your answer to 2 decimal places.

[3]
c.

Using your answer to part (b) and making your method clear, estimate

(i)

∫02(3t+4) dt \int_{0}^{2} (3^t + 4) \, dt ∫02​(3t+4)dt

(ii)

∫02(3t+1−3) dt \int_{0}^{2} (3^{t+1} - 3) \, dt ∫02​(3t+1−3)dt
[4]

Integration Questions

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

Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank