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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
