It is given that k k\,k is a positive constant and that ∫1k(32x+9)dx=8\displaystyle\int_1^k\left(\dfrac{3}{2\sqrt{x}} + 9\right)dx = 8∫1k(2x3+9)dx=8
Show that 9k+3k−20=09k + 3\sqrt{k} - 20 = 09k+3k−20=0.
Hence, using algebra, find the value of kkk.
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.