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.
26 exam-style questions on AQA A Level Maths 1.11.3 Definite integrals and areas. Each one has a worked solution and a mark scheme showing where the marks go.