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.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.