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.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
