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1.8 Integration

1.8 Integration

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Question 314

Figure 1 below shows the curve y=e2xy=e^{2x}y=e2x for x>0x>0x>0.

Figure for question 1

The interval [2,5][2,5][2,5] is divided into n n\,n equal strips of width δx=3n\displaystyle \delta x=\frac3nδx=n3​, and xi=2+iδxx_i=2+i\delta xxi​=2+iδx.

Find the exact value of

lim⁡n→∞∑i=1ne2xi δx\displaystyle\lim_{n\to\infty}\sum_{i=1}^{n} e^{2x_i}\,\delta xn→∞lim​i=1∑n​e2xi​δx.

[4]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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