It is given that k k\,k is a constant.
Find ∫(kx3+2x)dx\displaystyle\int\left(\dfrac{k}{x^3} + 2x\right)dx∫(x3k+2x)dx, giving your answer in its simplest form.
Find the value of k k\,k such that ∫12(kx3+2x)dx=12\displaystyle\int_1^2\left(\dfrac{k}{x^3} + 2x\right)dx = 12∫12(x3k+2x)dx=12
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.