The profile of a decorative architectural panel is modeled by a shaded region RRR. This region is defined by the following inequalities involving the vertical height y y\,y and horizontal distance xxx:
x2−8x+24≤y≤24−2x x^2 - 8x + 24 \le y \le 24 - 2x x2−8x+24≤y≤24−2xWhich of the following expressions correctly determines the area of the panel?
Select one box:
□∫06(x2−6x) dx\Box \int_{0}^{6} (x^2 - 6x) \, dx□∫06(x2−6x)dx
□∫06(6x−x2) dx\Box \int_{0}^{6} (6x - x^2) \, dx□∫06(6x−x2)dx
□∫06(x2−10x+48) dx\Box \int_{0}^{6} (x^2 - 10x + 48) \, dx□∫06(x2−10x+48)dx
□∫(24−2x) dx−∫(x2−8x+24) dx\Box \int (24 - 2x) \, dx - \int (x^2 - 8x + 24) \, dx□∫(24−2x)dx−∫(x2−8x+24)dx
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.