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Question 565

An architect is designing a decorative glass panel. In the design coordinate system, the upper profile of the panel is the curve y=15−2exy = 15 - 2e^xy=15−2ex and the lower profile is the curve y=e2xy = e^{2x}y=e2x. The region, representing the panel, is bounded by these two curves and the yyy-axis (the line x=0x = 0x=0), as shown shaded in the diagram below.

A coordinate diagram shows the region shaded between the upper curve y = 15 − 2eˣ, the lower curve y = e²ˣ, and the y-axis.

Show that the exact area of this panel is

15ln⁡3−8 15 \ln 3 - 8 15ln3−8

Fully justify your answer.

[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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