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1.8 Integration

1.8 Integration

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Question 216
i.

Find

∫x2e2x dx \int x^2e^{2x} \, dx ∫x2e2xdx
[4]
ii.

Use the substitution u=2x+1u = \sqrt{2x + 1}u=2x+1​ to show that

∫12x2x+1 dx=2(2x+1)12(Ax+B)+k \int \frac{12x}{\sqrt{2x + 1}} \, dx = 2(2x + 1)^{\frac{1}{2}}(Ax + B) + k ∫2x+1​12x​dx=2(2x+1)21​(Ax+B)+k

where AAA and BBB are integers to be found and kkk is an arbitrary constant.

[6]
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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