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TMUA 2018 · Paper 1 · Question 1 of 20

TMUA 2018 Paper 1 Question 1

Differentiation and integration — Definite integrals · fractional powers. Try it first; the answer and a full worked solution are below.

TMUA 2018 · Paper 1Differentiation and integrationDefinite integrals · fractional powers7 options
Find the value of ∫14 3 − 2xx√x dx
  1. A−132
  2. B−8516
  3. C−138
  4. D−1
  5. E−14
  6. F74
  7. G7
Show the answer and worked solution
answer · D
  1. A−132
  2. B−8516
  3. C−138
  4. D−1
  5. E−14
  6. F74
  7. G7
Do not try to integrate the quotient as it stands: split it first. Since x√x = x3/2, the integrand is 3x−3/2 − 2x−1/2. Integrating gives −6x−1/2 − 4x1/2, that is −6√x − 4√x. At x = 4 this is −3 − 8 = −11 and at x = 1 it is −6 − 4 = −10, so the integral is −11 − (−10) = −1.