The velocity v(t)v(t)v(t) of a microscopic probe moving through a fluid is modeled by the function
v(t)=10t2−34t,t>0 v(t) = \frac{10t^2 - 3}{4\sqrt{t}}, \quad t > 0 v(t)=4t10t2−3,t>0where vvv is measured in μm s−1\mu\text{m s}^{-1}μm s−1 and ttt is the time in seconds. At time t=1t = 1t=1, the displacement of the probe from a fixed origin is 4μm4 \mu\text{m}4μm. Find the displacement of the probe when t=9t = 9t=9.
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.