A robotic arm's velocity v(t)v(t)v(t), in ms−1\text{ms}^{-1}ms−1, at time t t\,t seconds is modelled by the function
v(t)=(4t−3)(t+2)6t,t>0 v(t) = \frac{(4\sqrt{t} - 3)(t + 2)}{6\sqrt{t}}, \quad t > 0 v(t)=6t(4t−3)(t+2),t>0Determine the general expression for the displacement, s(t)s(t)s(t), of the robotic arm, giving each term in its simplest form.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.