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Integration

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Question 4

The diagram shows part of the graph of y=12x13−6x13\displaystyle y = 12x^{\frac{1}{3}} - \frac{6}{x^{\frac{1}{3}}}y=12x31​−x31​6​

The shaded region is enclosed by the curve, the xxx-axis and the lines x=1x = 1x=1 and x=ax = ax=a, where a>1a > 1a>1

A Cartesian graph of the given curve with x- and y-axes, vertical boundaries at x = 1 and x = a, and the region between the boundaries shaded.

Given that the area of the shaded area is 180 square units, find the exact value of aaa.

[9]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

411 exam-style questions on Edexcel A Level Maths Integration, covering 13.1 Integrating x^n, 13.2 Indefinite Integrals, 13.3 Finding Functions, 13.4 Definite Integrals, 13.5 Areas under Curves, 13.6 Areas under the x-axis, and 13.7 Areas between curves and lines. Each one has a worked solution and a mark scheme showing where the marks go.

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