Worksheet: Integration by Substitution: Definite Integrals

In this worksheet, we will practice using integration by substitution for definite integrals.

Q1:

Use an appropriate substitution followed by a trigonometric one to evaluate 𝑦𝑦1+(𝑦)dln.

  • A l n 2 + 2
  • B l n 2 2
  • C l n 2
  • D l n 1 + 2
  • E l n ( 2 )

Q2:

Evaluate (2𝑟)𝑟d.

  • A 1 1 3
  • B 1 4
  • C81
  • D 8 1
  • E 1 4

Q3:

Determine 8𝑥8𝑥1𝑥d to the nearest hundredth.

Q4:

Evaluate 𝑥5𝑥+3𝑥d to the nearest thousandth.

Q5:

Find 𝑥𝑥+5𝑥d to the nearest thousandth.

Q6:

Determine 4𝑥(𝑥6)𝑥d rounded to one decimal place.

Q7:

Find 9(𝑧)(𝑧)𝑧tansecd.

  • A 9 2
  • B 9 2
  • C 9
  • D 1 2

Q8:

Determine 2𝑥+6𝑥d.

  • A12
  • B 4 3
  • C 4
  • D4

Q9:

Determine 5𝑥+7𝑥d.

  • A 5 0 7 + 5 0 5
  • B 1 0 7 + 1 0 5
  • C 2 0 7 + 2 0 5
  • D 1 0 5 + 1 0 7

Q10:

Evaluate 𝑥𝑥3𝑥d.

Q11:

Evaluate 8𝑡10𝑡+5𝑡d.

  • A 2 5 ( 2 7 ) l n
  • B 2 5 1 3 l n
  • C 8 5 ( 3 ) l n
  • D 2 5 ( 3 ) l n
  • E 8 5 ( 2 7 ) l n

Q12:

Evaluate 𝑒𝜃𝜃sincosd.

  • A 1 2 𝑒 1
  • B 2 𝑒 1
  • C 𝑒 2
  • D 1 2 1 𝑒
  • E 2 1 𝑒

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