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Lesson Worksheet: Integration by Substitution: Definite Integrals Mathematics • Higher Education

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

Q1:

Use the substitution ๐‘ข=๐‘ฅโˆ’4 to evaluate the definite integral ๏„ธ๐‘ฅ(๐‘ฅโˆ’4)๐‘ฅ๏Šฉ๏Šง๏Šจd.

  • A263
  • Bโˆ’443
  • Cโˆ’283
  • D283
  • E443

Q2:

Use the substitution ๐‘ข=1โˆ’12(๐‘ฅ)sin to evaluate the definite integral ๏„ธ(๐‘ฅ)๏„ž1โˆ’12(๐‘ฅ)๐‘ฅ๏‘ฝ๏Žก๏Šฆcossind.

  • A4โˆ’โˆš23
  • Bโˆ’43โˆ’โˆš2โˆš3
  • C4โˆ’โˆš22
  • Dโˆ’4โˆ’โˆš23
  • E43โˆ’โˆš2โˆš3

Q3:

Evaluate ๏„ธ๐‘ฅ๏€น๐‘ฅโˆ’3๏…๐‘ฅ๏Šจ๏Šง๏Šจ๏Šฉ๏Šฉd.

Q4:

Find ๏„ธ๐‘ฅโˆš๐‘ฅ+5๐‘ฅ๏Šช๏Šฑ๏Šงd to the nearest thousandth.

Q5:

Determine ๏„ธ2โˆš๐‘ฅ+6๐‘ฅ๏Šฑ๏Šจ๏Šฑ๏Šซd.

  • A12
  • B43
  • Cโˆ’4
  • D4

Q6:

Evaluate ๏„ธ2๏€ป4โˆ’๐‘ฅ6๏‡๏€ป4โˆ’๐‘ฅ6๏‡๏Šจ๏Šช๏Šจ๏Šช๏Šฑ๏Ž„tansec, giving an exact answer.

  • A8โˆš3โˆ’12
  • B6โˆš3โˆ’12
  • C6โˆš3
  • D12โˆ’8โˆš3
  • E8โˆš3

Q7:

Find ๏„ธโˆ’9(๐‘ง)(๐‘ง)๐‘ง๏‘ฝ๏Žฃ๏Šฆ๏Šจtansecd.

  • A92
  • Bโˆ’92
  • Cโˆ’9
  • D12

Q8:

Determine ๏„ธ๐‘ฅ๐‘ฅ๐‘ฅ๏Œพ๏Šงlnd.

  • A14
  • B2
  • C1
  • D4
  • E12

Q9:

Evaluate ๏„ธ5๐‘ฅโˆ’7๏€บ๏€บ(๐‘ฅโˆ’7)๏†+1๏†๐‘ฅ๏Šญ๏Šฐ๏Œพ๏Šฎ๏Šจ๏Šฉlnd.

  • A50
  • B51.25
  • C2053
  • D10
  • E20,900๐‘’

Q10:

Evaluate ๏„ธ๐‘’๐œƒ๐œƒ๏Ž„๏Šจ๏ผ๏‘ฝ๏Žขsincosd.

  • A12๏€ป๐‘’โˆ’1๏‡โˆš๏Šฉ
  • B2๏€ป๐‘’โˆ’1๏‡โˆš๏Šฉ
  • C๐‘’2โˆš๏Šฉ
  • D12๏€ป1โˆ’๐‘’๏‡โˆš๏Šฉ
  • E2๏€ป1โˆ’๐‘’๏‡โˆš๏Šฉ

This lesson includes 11 additional questions and 144 additional question variations for subscribers.

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