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.
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.