The rate of change of the mass of a substance in a chemical reaction, M′(t)M'(t)M′(t) in grams per hour, is modeled by the function:
M′(t)=18t3t+4,0≤t≤4 M'(t) = \frac{18t}{\sqrt{3t+4}}, \quad 0 \le t \le 4 M′(t)=3t+418t,0≤t≤4Using the substitution u=3t+4u = \sqrt{3t+4}u=3t+4, find the exact change in mass, in grams, between t=0t = 0t=0 and t=4t = 4t=4.
In a separate experiment, the pressure within a vessel is found to vary according to the function:
f(p)=6p2−11(p−1)(3p+2) f(p) = \frac{6p^2 - 11}{(p - 1)(3p + 2)} f(p)=(p−1)(3p+2)6p2−11Find ∫f(p) dp\int f(p) \, dp∫f(p)dp.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.