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Worksheet: Evaluating the Definite Integrals of Polynomials Using the Power Rule

Q1:

Let 𝑓 ( π‘₯ ) = 6 π‘₯ + 1 2 . Evaluate the definite integral of 𝑓 from π‘₯ = 2 to π‘₯ = 3 .

Q2:

Let 𝑓 ( π‘₯ ) = 6 π‘₯ βˆ’ 4 2 . Evaluate the definite integral of 𝑓 from π‘₯ = 2 to π‘₯ = 3 .

Q3:

Evaluate ο„Έ ο€Ή 8 𝑣 + 1 2 𝑣 + 3  𝑣 1 0 7 3 d .

Q4:

Evaluate ο„Έ ο€Ή 1 6 𝑣 + 4 𝑣 βˆ’ 4  𝑣 1 0 7 3 d .

Q5:

Evaluate ο„Έ ο€Ό 4 5 𝑑 + 3 4 𝑑 βˆ’ 2 3 𝑑  𝑑 1 0 3 2 d .

  • A βˆ’ 1 4 0
  • B 5 3 6 0
  • C βˆ’ 7 6 0
  • D 7 6 0
  • E βˆ’ 5 3 6 0

Q6:

Evaluate ο„Έ ο€Ό 4 3 𝑑 βˆ’ 3 4 𝑑 βˆ’ 2 3 𝑑  𝑑 2 1 3 2 d .

  • A βˆ’ 4 3 7 2
  • B 5 1 4
  • C βˆ’ 9 4
  • D 9 4
  • E βˆ’ 5 1 4

Q7:

Evaluate ο„Έ 4 π‘₯ π‘₯ 2 7 1 βˆ’ 2 3 d .

Q8:

Evaluate ο„Έ ( 𝑒 + 2 ) ( 𝑒 + 1 ) 𝑒 1 βˆ’ 2 d .

  • A 1 1 2
  • B6
  • C βˆ’ 6
  • D 9 2
  • E βˆ’ 9 2

Q9:

Evaluate ο„Έ ( 5 𝑒 βˆ’ 3 ) ( 𝑒 + 5 ) 𝑒 1 βˆ’ 2 d .

  • A 1 9 2
  • B βˆ’ 6 6
  • C66
  • D βˆ’ 6 3
  • E63

Q10:

Determine ο„Έ 3 π‘₯ ο€Ή βˆ’ 3 π‘₯ + 1  π‘₯ 1 0 2 2 d .

  • A54
  • B βˆ’ 9
  • C486
  • D 3 2