An architectural feature for a new gallery is designed with a side profile following the curve y=32x3y = \frac{3}{2}x^3y=23x3. To calculate the volume of concrete required, an engineer first determines the total cross-sectional area between the curve and the xxx-axis for two distinct sections:
Section A is bounded by the curve, the xxx-axis, and the vertical lines x=−3x = -3x=−3 and x=−1x = -1x=−1.
Section B is bounded by the curve, the xxx-axis, and the vertical lines x=2x = 2x=2 and x=4x = 4x=4.
Calculate the total area of these two sections.
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.