The region S S\,S is bounded by the curves y=e2xy = e^{2x}y=e2x and y=15−2exy = 15 - 2e^xy=15−2ex, and the vertical line x=0x = 0x=0. These curves intersect at a point in the first quadrant.
Show that the exact area of the region S S\,S is
15ln3−8 15 \ln 3 - 8 15ln3−8Fully justify your answer.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.