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Question 106

The region enclosed by the yyy-axis, y=e2xy = e^{2x}y=e2x and y=30−exy = 30 - e^xy=30−ex is shown on the diagram.

A graph showing the region enclosed by the y-axis, the curves y = e²ˣ and y = 30 − eˣ, with the enclosed region shaded.

A graph showing the region enclosed by the y-axis, the curve y=e2xy = e^{2x}y=e2x, and the curve y=30−exy = 30 - e^xy=30−ex. The region is shaded. The x-axis and y-axis are shown, with the origin labeled O. The curve y=e2xy = e^{2x}y=e2x is an increasing exponential curve starting from the y-axis. The curve y=30−exy = 30 - e^xy=30−ex is a decreasing exponential curve starting from the y-axis. They intersect at a point in the first quadrant. The shaded region is bounded by the y-axis, the curve y=e2xy = e^{2x}y=e2x, and the curve y=30−exy = 30 - e^xy=30−ex.

Find the exact area of the shaded region.

[10]
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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