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=∫214x2x−1dx=15917Fully justify your answer.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) 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.
