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TMUA 2021 · Paper 1 · Question 10 of 20

TMUA 2021 Paper 1 Question 10

Differentiation and integration — Trapezium rule · combining logarithms. Try it first; the answer and a full worked solution are below.

TMUA 2021 · Paper 1Differentiation and integrationTrapezium rule · combining logarithms6 options
Use the trapezium rule with 3 strips to estimate ∫122 2log10 x dx
  1. Alog10√62
  2. Blog1032
  3. Clog1094
  4. Dlog10 3
  5. Elog108116
  6. Flog10√232
Show the answer and worked solution
answer · B
  1. Alog10√62
  2. Blog1032
  3. Clog1094
  4. Dlog10 3
  5. Elog108116
  6. Flog10√232
Three strips across [12,  2] have width h = 1.53 = 12, with ordinates at x = 12,  1,  32,  2, namely 2log1012, 0, 2log1032 and 2log10 2. The rule gives h2[y0 + 2(y1 + y2) + y3] = 14[2log1012 + 4log1032 + 2log102]. Now use the log laws: 12log1012 + 12log102 = 12log10 1 = 0, so everything collapses to the middle term, log1032.