Find ∫(2x−x2)dx\displaystyle\int\left(2x - x^2\right)dx∫(2x−x2)dx.
Evaluate ∫04(2x−x2)dx\displaystyle\int_0^4\left(2x - x^2\right)dx∫04(2x−x2)dx.
Using a sketch, explain why the integral in part (b) does not give the area enclosed between the curve y=2x−x2y = 2x - x^2y=2x−x2 and the xxx-axis.
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.