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
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
