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.
Show that the exact area of this panel is
15ln3−8 15 \ln 3 - 8 15ln3−8Fully justify your answer.
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.
