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=91715W = \int_{\frac{1}{2}}^{4} x\sqrt{2x-1} \, dx = \frac{91\sqrt{7}}{15}W=∫214x2x−1dx=15917
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Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.