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TMUA 2022 · Paper 1 · Question 6 of 20

TMUA 2022 Paper 1 Question 6

Differentiation and integration — Definite integrals with logarithmic limits. Try it first; the answer and a full worked solution are below.

TMUA 2022 · Paper 1Differentiation and integrationDefinite integrals with logarithmic limits7 options
Given that ∫log2 5log2 20 x dx = log2 M what is the value of M?
  1. A4
  2. B15
  3. C16
  4. D20
  5. E25
  6. F100
  7. G10 000
Show the answer and worked solution
answer · F
  1. A4
  2. B15
  3. C16
  4. D20
  5. E25
  6. F100
  7. G10 000
The integral is [x22], giving 12[(log2 20)2 − (log2 5)2]. Factorising the difference of two squares, this is 12(log2 20 − log2 5)(log2 20 + log2 5) = 12(log2 4)(log2 100) = log2 100. So M = 100.