The rate of increase of a substance's temperature, T T\,T in degrees Celsius, over time t t\,t minutes is modeled by the equation
dTdt=52t+3,t≥0 \frac{dT}{dt} = \frac{5}{2t + 3}, \quad t \ge 0 dtdT=2t+35,t≥0Calculate the exact change in temperature between t=1t = 1t=1 and t=6t = 6t=6 minutes, giving your answer in its simplest form.
g(x)=2x3−11x2−8x+87(x−4)2g(x) = \dfrac{2x^3 - 11x^2 - 8x + 87}{(x - 4)^2}g(x)=(x−4)22x3−11x2−8x+87 for x>4x > 4x>4.
Given that g(x)=Ax+B+C(x−4)2g(x) = Ax + B + \dfrac{C}{(x - 4)^2}g(x)=Ax+B+(x−4)2C where AAA, B B\,B and C C\,C are constants to be determined, find
∫g(x) dx \int g(x) \, dx ∫g(x)dxPractise 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.
