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TMUA 2021 · Paper 2 · Question 1 of 20

TMUA 2021 Paper 2 Question 1

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

TMUA 2021 · Paper 2Differentiation and integrationDefinite integrals · fractional and negative powers7 options
Find the value of ∫14(3√x + 4x2)dx
  1. A−0.75
  2. B7.125
  3. C11
  4. D17
  5. E18
  6. F21.875
  7. G34.5
Show the answer and worked solution
answer · D
  1. A−0.75
  2. B7.125
  3. C11
  4. D17
  5. E18
  6. F21.875
  7. G34.5
Write the integrand as powers before integrating: 3x1/2 + 4x−2. Then ∫ 3x1/2dx = 2x3/2 and ∫ 4x−2dx = −4x, so the antiderivative is 2x3/2 − 4x. At x=4 this is 2× 8 − 1 = 15; at x=1 it is 2 − 4 = −2. The value is 15 − (−2) = 17.