Given that k k\,k is a positive constant,
find
∫8x2x2+k dx \int \frac{8x}{2x^2 + k} \, dx ∫2x2+k8xdxGiven also that
∫148x2x2+k dx=ln81 \int_{1}^{4} \frac{8x}{2x^2 + k} \, dx = \ln 81 ∫142x2+k8xdx=ln81find the value of kkk.
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.
