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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 223

A robotic arm's force output FFF, in Newtons, is modeled by F(x)=x2x−1F(x) = x\sqrt{2x-1}F(x)=x2x−1​ where xxx is the extension in metres. Use integration by substitution to show that the total work done WWW during an extension from x=12x = \frac{1}{2}x=21​ to x=4x = 4x=4 is given by

W=∫124x2x−1 dx=91715 W = \int_{\frac{1}{2}}^{4} x\sqrt{2x-1} \, dx = \frac{91\sqrt{7}}{15} W=∫21​4​x2x−1​dx=15917​​

Fully justify your answer.

[7]
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3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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