Given that k k\,k is a constant
Find ∫(kx3+2x)dx\displaystyle \int \left( \frac{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( \frac{k}{x^3} + 2x \right) dx = 12∫12(x3k+2x)dx=12
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
