A synthetic crystal's mass growth rate, dmdt\displaystyle \frac{dm}{dt}dtdm in grams per hour, is modeled by the equation:
dmdt=15t3−45t,t>0 \frac{dm}{dt} = \frac{15t^3 - 4}{5\sqrt{t}}, \quad t > 0 dtdm=5t15t3−4,t>0where t t\,t is the time elapsed in hours. Determine the general expression for the mass m m\,m in terms of ttt, giving your answer 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.