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Question 482
a.

Use the substitution x=u2+1x = u^2 + 1x=u2+1 to show that

∫2102 dx(x−1)(2+x−1)=∫qp4 duu(u+2) \int_2^{10} \frac{2 \, dx}{(x-1)(2+\sqrt{x-1})} = \int_q^p \frac{4 \, du}{u(u+2)} ∫210​(x−1)(2+x−1​)2dx​=∫qp​u(u+2)4du​

where p p\,p and q q\,q are positive constants to be found.

[4]
b.

Hence, using algebraic integration, show that

∫2102 dx(x−1)(2+x−1)=ln⁡a \int_2^{10} \frac{2 \, dx}{(x-1)(2+\sqrt{x-1})} = \ln a ∫210​(x−1)(2+x−1​)2dx​=lna

where a a\,a is a rational constant to be found.

[6]
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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