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TMUA 2023 · Paper 2 · Question 2 of 20

TMUA 2023 Paper 2 Question 2

Differentiation and integration — Definite integrals · difference of two squares. Try it first; the answer and a full worked solution are below.

TMUA 2023 · Paper 2Differentiation and integrationDefinite integrals · difference of two squares8 options
Evaluate ∫916(1√x + √x)2 dx  − ∫916(1√x − √x)2 dx
  1. A0
  2. B2
  3. C4
  4. D7
  5. E14
  6. F28
  7. G75
  8. H175
Show the answer and worked solution
answer · F
  1. A0
  2. B2
  3. C4
  4. D7
  5. E14
  6. F28
  7. G75
  8. H175
Combine the integrals before doing any work. With a = 1√ x and b = √ x, the integrand is (a+b)2 − (a−b)2 = 4ab = 4⋅1√ x⋅√ x = 4. So the value is ∫916 4 dx = 4(16−9) = 28.