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
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.