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1.11 H: Integration

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Question 54

It is given that k k\,k is a constant.

a.

Find ∫(kx3+2x)dx\displaystyle\int\left(\dfrac{k}{x^3} + 2x\right)dx∫(x3k​+2x)dx, giving your answer in its simplest form.

[3]
b.

Find the value of k k\,k such that ∫12(kx3+2x)dx=12\displaystyle\int_1^2\left(\dfrac{k}{x^3} + 2x\right)dx = 12∫12​(x3k​+2x)dx=12

[3]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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