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Question 486

The table below shows corresponding values of x x\,x and y y\,y for y=2+x1+x\displaystyle y = \sqrt{\frac{2+x}{1+x}}y=1+x2+x​​

The values of y y\,y are given to 4 significant figures.

xxx00.511.52
yyy1.4141.2911.2251.1831.155
a.

Use the trapezium rule, with all the values of y y\,y in the table, to find an estimate for

∫022+x1+xdx \int_0^2 \sqrt{\frac{2+x}{1+x}} dx ∫02​1+x2+x​​dx

giving your answer to 3 significant figures.

[3]
b.

Using your answer to part (a), deduce an estimate for ∫028+4x1+xdx\displaystyle \int_0^2 \sqrt{\frac{8+4x}{1+x}} dx∫02​1+x8+4x​​dx

[1]
Markscheme

Integration Questions

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

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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