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1.11.5 Integration by substitution and by parts (A-level only)

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Question 79

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.

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1.11.5 Integration by substitution and by parts (A-level only) Questions

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