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Question 415

A coordinate diagram shows the curve y = e²ˣ for x > 0, a point P(x, y), and a shaded rectangle of height y and width δx.

The diagram shows the curve y=e2xy = e^{2x}y=e2x, x>0x > 0x>0. The point P(x,y)P(x, y)P(x,y) lies on the curve. The rectangle, shown shaded on the diagram, has height y y\,y and width δx\delta xδx.

Calculate, giving your answer in exact form

lim⁡δx→0∑x=25e2xδx \lim_{\delta x \rightarrow 0} \sum_{x=2}^5 e^{2x} \delta x δx→0lim​x=2∑5​e2xδx
[3]
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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