The profile of a decorative glass panel is modeled by the curve y=23x3\displaystyle y = \frac{2}{3}x^3y=32x3. The design requires two specific regions of the panel to be tinted.
Region 1 is bounded by the curve, the xxx-axis, and the vertical lines x=−3x = -3x=−3 and x=−1x = -1x=−1.
Region 2 is bounded by the curve, the xxx-axis, and the vertical lines x=0x = 0x=0 and x=2x = 2x=2.
Find the total area of the tinted regions.
10.67
13.33
16.00
18.67
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.