Integration
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Question 383
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.
(a).[1]
Show that
limδx→0∑x=25e2xδx=∫25e2xdx \lim_{\delta x \rightarrow 0} \sum_{x=2}^5 e^{2x} \delta x = \int_2^5 e^{2x} dx δx→0limx=2∑5e2xδx=∫25e2xdx(b).[2]
Hence calculate
limδx→0∑x=25e2xδx \lim_{\delta x \rightarrow 0} \sum_{x=2}^5 e^{2x} \delta x δx→0limx=2∑5e2xδxIntegration Questions
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.