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1.11 H: Integration

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Question 242

The profile of a decorative glass panel is modeled by the curve y=23x3\displaystyle y = \frac{2}{3}x^3y=32​x3. 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

[5]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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