f(x)=2x3−x2−8x+4f(x) = 2x^3 - x^2 - 8x + 4f(x)=2x3−x2−8x+4
Use the factor theorem to show that (x+2)(x + 2)(x+2) is a factor of f(x)f(x)f(x)
Hence, showing all your working, write f(x)f(x)f(x) as a product of three linear factors.
The finite region R R\,R is bounded by the curve with equation y=f(x)y = f(x)y=f(x) and the xxx-axis, and lies below the xxx-axis. Find, using algebraic integration, the exact value of the area of RRR.
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.