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.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
