A function f f\,f has domain R\mathbb{R}R and range {y∈R:y≥−4}\{y \in \mathbb{R} : y \ge -4\}{y∈R:y≥−4}. The gradient of the curve y=f(x)y = f(x)y=f(x) at any point (x,y)(x, y)(x,y) is given by dydx=(2x−8)ex\displaystyle \frac{dy}{dx} = (2x - 8)e^xdxdy=(2x−8)ex. Find an expression for f(x)f(x)f(x). Fully justify your answer.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.