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1.8 Integration

1.8 Integration

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Question 191
i.

Find

[∫36(3−4x)2 dx [\int \frac{36}{(3 - 4x)^2} \, dx [∫(3−4x)236​dx

] giving your answer in simplest form.

[2]
ii a.

Express 4x+71−2x\frac{4x + 7}{1 - 2x}1−2x4x+7​ in the form

A+B1−2x where A and B are constants to be found. A + \frac{B}{1 - 2x} \text{ where } A \text{ and } B \text{ are constants to be found.} A+1−2xB​ where A and B are constants to be found.
[2]
ii b.

Hence find, using algebraic integration, the exact value of

[∫−404x+71−2x dx [\int_{-4}^{0} \frac{4x + 7}{1 - 2x} \, dx [∫−40​1−2x4x+7​dx

] giving your answer in the form aln⁡b−ca\ln b - calnb−c, where a,b,a, b,a,b, and ccc are integers.

[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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