Find, using algebraic integration, the exact value of
∫16102x+3dx \int_{1}^{6} \frac{10}{2x + 3} dx ∫162x+310dxgiving your answer in simplest form.
The rate of oxygen consumption in a bioreactor, G(t)G(t)G(t), is modeled by the function G(t)=2t3−7t2−12t+52(t−3)2G(t) = \frac{2t^3 - 7t^2 - 12t + 52}{(t - 3)^2}G(t)=(t−3)22t3−7t2−12t+52 for t>3t > 3t>3.
Given that G(t)=At+B+C(t−3)2G(t) = At + B + \frac{C}{(t - 3)^2}G(t)=At+B+(t−3)2C where AAA, BBB and CCC are constants to be found, find
∫G(t)dt \int G(t) dt ∫G(t)dtPractise 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.
