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.
119 exam-style questions on CCEA A Level Maths 3.6.4 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.