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1.11 H: Integration

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Question 82

It is given that k k\,k is a positive constant and that ∫1k(32x+9)dx=8\displaystyle\int_1^k\left(\dfrac{3}{2\sqrt{x}} + 9\right)dx = 8∫1k​(2x​3​+9)dx=8

a.

Show that 9k+3k−20=09k + 3\sqrt{k} - 20 = 09k+3k​−20=0.

[4]
b.

Hence, using algebra, find the value of kkk.

[4]
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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