The mass of a biochemical sample MMM (measured in milligrams) varies over time ttt (measured in seconds, t>0t > 0t>0) according to a growth model. The mass-time curve passes through the point P(4,15)P(4, 15)P(4,15).
Given that
dMdt=5t2−402t \frac{\mathrm{d} M}{\mathrm{d} t} = \frac{5t^2 - 40}{2\sqrt{t}} dtdM=2t5t2−40Determine the equation of the tangent to the curve at the point PPP, writing your answer in the form M=kt+cM = kt + cM=kt+c, where kkk and ccc are integers to be found.
Find the function M(t)M(t)M(t).
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.