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.

  • Aln2+2
  • Bln22
  • Cln2
  • Dln1+2
  • Eln(2)

Q2:

Evaluate (2𝑟)𝑟d.

  • A113
  • B14
  • C81
  • D81
  • E14

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.

  • A92
  • B92
  • C9
  • D12

Q8:

Determine 2𝑥+6𝑥d.

  • A12
  • B43
  • C4
  • D4

Q9:

Determine 5𝑥+7𝑥d.

  • A507+505
  • B107+105
  • C207+205
  • D105+107

Q10:

Evaluate 𝑥𝑥3𝑥d.

Q11:

Evaluate 8𝑡10𝑡+5𝑡d.

  • A25(27)ln
  • B2513ln
  • C85(3)ln
  • D25(3)ln
  • E85(27)ln

Q12:

Evaluate 𝑒𝜃𝜃sincosd.

  • A12𝑒1
  • B2𝑒1
  • C𝑒2
  • D121𝑒
  • E21𝑒

Q13:

Evaluate 24𝑥64𝑥6tansec, giving an exact answer.

  • A8312
  • B6312
  • C63
  • D1283
  • E83

Q14:

Evaluate 5𝑥7(𝑥7)+1𝑥lnd.

  • A50
  • B51.25
  • C2053
  • D10
  • E20,900𝑒

Q15:

Evaluate 4𝑥𝜋6𝑥𝑥sind.

  • A8𝜋
  • B16𝜋
  • C8𝜋
  • D8𝜋
  • E8𝜋

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