Atividade: Integrais Indefinidas de Funções

Nesta atividade, nós vamos praticar a encontrar as integrais indefinidas de funções.

Q1:

Determine ๏„ธ๏€น10๐‘ฅ+21๐‘ฅโˆ’49๏…๐‘ฅ๏Šจd.

  • A 3 0 ๐‘ฅ + 4 2 ๐‘ฅ โˆ’ 4 9 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • B 1 0 ๐‘ฅ + C
  • C 1 0 3 ๐‘ฅ + 2 1 2 ๐‘ฅ โˆ’ 4 9 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • D 1 0 ๐‘ฅ + 2 1 ๐‘ฅ โˆ’ 4 9 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • E 5 ๐‘ฅ + 2 1 ๐‘ฅ โˆ’ 4 9 ๐‘ฅ + ๏Šฉ ๏Šจ C

Q2:

Determine ๏„ธ๏€ผโˆ’4โˆš๐‘ฅโˆ’5+7๐‘ฅ๏ˆ๐‘ฅ๏Šจd.

  • A โˆ’ 5 ๐‘ฅ โˆ’ 8 โˆš ๐‘ฅ + 7 ๐‘ฅ + ๏Šฉ C
  • B โˆ’ 4 ๐‘ฅ + 7 ๐‘ฅ + ๏Šจ C
  • C โˆ’ 5 ๐‘ฅ โˆ’ 8 โˆš ๐‘ฅ 3 โˆ’ 7 ๐‘ฅ + ๏Šฉ C
  • D โˆ’ 8 โˆš ๐‘ฅ โˆ’ 7 ๐‘ฅ + C

Q3:

Determine ๏„ธ๐‘ฅโˆ’14๐‘ฅ๐‘ฅโˆ’14๐‘ฅ๏Šช๏Šฉd.

  • A 3 ๐‘ฅ + ๏Šช C
  • B 1 3 ๐‘ฅ + ๏Šช C
  • C 1 4 ๐‘ฅ + ๏Šช C
  • D ๐‘ฅ + ๏Šช C
  • E 4 ๐‘ฅ + ๏Šช C

Q4:

Determine ๏„ธ๏€ผ๐‘ฅโˆ’5๐‘ฅ๏ˆ๏€ผ๐‘ฅ+5๐‘ฅ๏ˆ๏€ผ๐‘ฅ+25๐‘ฅ๏ˆ๐‘ฅ๏Šจ๏Šจd.

  • A ๐‘ฅ 4 + 6 2 5 4 ๐‘ฅ + ๏Šซ ๏Šฉ C
  • B ๐‘ฅ 5 โˆ’ 6 2 5 3 ๐‘ฅ + ๏Šซ ๏Šฉ C
  • C ๐‘ฅ 5 + 6 2 5 3 ๐‘ฅ + ๏Šซ ๏Šฉ C
  • D ๐‘ฅ 3 + 1 2 5 ๐‘ฅ + ๏Šฉ ๏Šซ C

Q5:

Determine ๏„ธ๏€ผ3๐‘ฅโˆ’7๐‘ฅ๏ˆ๐‘ฅ๏Šจd.

  • A ๏€ผ 3 ๐‘ฅ โˆ’ 7 ๐‘ฅ ๏ˆ + ๏Šฉ C
  • B 9 ๐‘ฅ โˆ’ 4 2 ๐‘ฅ + 4 9 ๐‘ฅ + ๏Šฉ C
  • C 1 3 ๏€ผ 3 ๐‘ฅ โˆ’ 7 ๐‘ฅ ๏ˆ + ๏Šฉ C
  • D 3 ๐‘ฅ โˆ’ 4 2 ๐‘ฅ โˆ’ 4 9 ๐‘ฅ + ๏Šฉ C

Q6:

Determine ๏„ธ4๐‘ฅ+๐‘ฅ+12๐‘ฅ+1๐‘ฅ๏Šฉd.

  • A 6 ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๐‘ฅ + ๏Šฉ ๏Šจ C
  • B 2 ๐‘ฅ โˆ’ ๐‘ฅ + ๐‘ฅ + ๏Šฉ ๏Šจ C
  • C 2 ๐‘ฅ 3 โˆ’ ๐‘ฅ 2 + ๐‘ฅ + ๏Šฉ ๏Šจ C
  • D ๐‘ฅ โˆ’ ๐‘ฅ + ๐‘ฅ + ๏Šฉ ๏Šจ C

Q7:

Determine ๏„ธ๏„Ÿ๏€ผ8๐‘ฅโˆ’18๐‘ฅ๏ˆ+4๐‘ฅ๏Šจ๏Šจ๏Šจd.

  • A 2 4 ๐‘ฅ โˆ’ 1 8 ๐‘ฅ + ๏Šฉ ๏Šฑ ๏Šง C
  • B 8 ๐‘ฅ โˆ’ 1 2 4 ๐‘ฅ + ๏Šฑ ๏Šฉ C
  • C 8 ๐‘ฅ + 1 8 ๐‘ฅ + ๏Šฉ ๏Šฑ ๏Šง C
  • D 4 ๐‘ฅ โˆ’ 1 1 6 ๐‘ฅ + ๏Šฉ ๏Šฑ ๏Šง C
  • E 8 3 ๐‘ฅ โˆ’ 1 8 ๐‘ฅ + ๏Šฉ ๏Šฑ ๏Šง C

Q8:

Determine ๏„ธ36๐‘ฅโˆ’49โˆš๐‘ฅ(6๐‘ฅ+7)๐‘ฅ๏Šจ๏Žงd.

  • A 4 5 ๐‘ฅ 4 โˆ’ 4 9 ๐‘ฅ 8 + ๏Ž  ๏Žค ๏Žง ๏Žฆ ๏Žง C
  • B 6 ๐‘ฅ โˆ’ 7 ๐‘ฅ + ๏Ž  ๏Žค ๏Žง ๏Žฆ ๏Žง C
  • C 1 6 ๐‘ฅ 5 โˆ’ 8 ๐‘ฅ + ๏Ž  ๏Žค ๏Žง ๏Žฆ ๏Žง C
  • D 4 8 ๐‘ฅ 7 + 5 6 ๐‘ฅ + ๏Ž  ๏Žค ๏Žง ๏Žฆ ๏Žง C

Q9:

Determine ๏„ธ(4๐‘ฅ+1)(2๐‘ฅโˆ’6)๐‘ฅd.

  • A 8 ๐‘ฅ + C
  • B 4 ๐‘ฅ โˆ’ 2 2 ๐‘ฅ โˆ’ 6 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • C 8 3 ๐‘ฅ โˆ’ 1 1 ๐‘ฅ โˆ’ 6 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • D 2 4 ๐‘ฅ โˆ’ 4 4 ๐‘ฅ โˆ’ 6 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • E 8 ๐‘ฅ โˆ’ 2 2 ๐‘ฅ โˆ’ 6 ๐‘ฅ + ๏Šฉ ๏Šจ C

Q10:

Determine ๏„ธ๐‘ฅโˆ’19๐‘ฅ+70๐‘ฅโˆ’14๐‘ฅ๏Šจd.

  • A ๐‘ฅ 2 โˆ’ 1 4 ๐‘ฅ + ๏Šจ C
  • B ๐‘ฅ 3 โˆ’ 1 9 ๐‘ฅ 2 + 7 0 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • C 1 2 ๏€น ๐‘ฅ โˆ’ 1 9 ๐‘ฅ + 7 0 ๏… + ๏Šจ ๏Šจ C
  • D ๐‘ฅ 2 โˆ’ 5 ๐‘ฅ + ๏Šจ C

Q11:

Determine ๏„ธ(๐‘ฅ+4)๏€น๐‘ฅโˆ’4๐‘ฅ+16๏…๐‘ฅ๏Šจd.

  • A 4 ๐‘ฅ + 6 4 ๐‘ฅ + ๏Šช C
  • B ๐‘ฅ 4 + 6 4 ๐‘ฅ + ๏Šช C
  • C ๐‘ฅ 3 + 6 4 ๐‘ฅ + ๏Šช C
  • D ๐‘ฅ 2 + 6 4 ๐‘ฅ + ๏Šจ C

Q12:

Determine ๏„ธ(๐‘ฅโˆ’6)(๐‘ฅโˆ’5)(๐‘ฅโˆ’3)๐‘ฅd.

  • A ๐‘ฅ โˆ’ 1 4 ๐‘ฅ + 6 3 ๐‘ฅ โˆ’ 9 0 + ๏Šฉ ๏Šจ C
  • B 1 8 ( ๐‘ฅ โˆ’ 6 ) ( ๐‘ฅ โˆ’ 5 ) ( ๐‘ฅ โˆ’ 3 ) + ๏Šจ ๏Šจ ๏Šจ C
  • C ๐‘ฅ โˆ’ 1 4 ๐‘ฅ + 6 3 ๐‘ฅ โˆ’ 9 0 ๐‘ฅ + ๏Šช ๏Šฉ ๏Šจ C
  • D ๐‘ฅ 4 โˆ’ 1 4 ๐‘ฅ 3 + 6 3 ๐‘ฅ 2 โˆ’ 9 0 ๐‘ฅ + ๏Šช ๏Šฉ ๏Šจ C

Q13:

Determine ๏„ธโˆ’27๐‘ฅ๐‘ฅ๏Šฑ๏Šฏd.

  • A 1 2 8 ๐‘ฅ + ๏Šฑ ๏Šฎ C
  • B 1 3 5 ๐‘ฅ + ๏Šฑ ๏Šง ๏Šฆ C
  • C 1 6 7 ๐‘ฅ + ๏Šฑ ๏Šฎ C
  • D โˆ’ 2 7 ๐‘ฅ + ๏Šฑ ๏Šฎ C
  • E 2 6 3 ๐‘ฅ + ๏Šฑ ๏Šฎ C

Q14:

Determine ๏„ธโˆ’9๐‘ฅ+79๐‘ฅ๐‘ฅ๏Šจ๏Šจd.

  • A 7 9 ๐‘ฅ + C
  • B โˆ’ ๐‘ฅ โˆ’ 7 9 ๐‘ฅ + ๏Šจ C
  • C โˆ’ ๐‘ฅ + 7 9 ๐‘ฅ + C
  • D โˆ’ 7 9 ๐‘ฅ + C

Q15:

Determine ๏„ธ๏’(โˆ’9๐‘ฅ+10)โˆ’8๏ž๐‘ฅ๏Šจd.

  • A โˆ’ 8 ๐‘ฅ + 1 3 ( โˆ’ 9 ๐‘ฅ + 1 0 ) + ๏Šฉ C .
  • B โˆ’ 8 ๐‘ฅ โˆ’ 1 2 7 ( โˆ’ 9 ๐‘ฅ + 1 0 ) + ๏Šฉ C .
  • C โˆ’ 8 ๐‘ฅ โˆ’ 1 8 ( โˆ’ 9 ๐‘ฅ + 1 0 ) + ๏Šจ C .
  • D โˆ’ 2 4 ๐‘ฅ โˆ’ 2 7 ( โˆ’ 9 ๐‘ฅ + 1 0 ) + ๏Šฉ C .

Q16:

Determine ๏„ธ๏€ผ8โˆš๐‘ฅโˆ’1๐‘ฅ๏ˆ๐‘ฅ๏Šชd.

  • A 8 โˆš ๐‘ฅ โˆ’ 1 ๐‘ฅ + ๏Šฉ ๏Šฉ C
  • B 1 2 โˆš ๐‘ฅ + 3 ๐‘ฅ + ๏Šฉ ๏Šฉ C
  • C 1 6 3 โˆš ๐‘ฅ + 1 3 ๐‘ฅ + ๏Šฉ ๏Šฉ C
  • D 1 6 โˆš ๐‘ฅ + 1 4 ๐‘ฅ + ๏Šฉ ๏Šฉ C
  • E โˆ’ 1 6 โˆš ๐‘ฅ + 1 5 ๐‘ฅ + ๏Šซ C

Q17:

Determine ๏„ธ7โˆš๐‘ฅ๐‘ฅ๏Šฉd.

  • A 7 โˆš ๐‘ฅ + ๏Šซ C
  • B 7 0 โˆš ๐‘ฅ + ๏Šซ C
  • C 1 4 โˆš ๐‘ฅ + C
  • D 1 4 5 โˆš ๐‘ฅ + ๏Šซ C
  • E 1 4 3 โˆš ๐‘ฅ + ๏Šซ C

Q18:

Determine ๏„ธ๐‘ฅ๏€น๐‘ฅ+2๏…๐‘ฅ๏Šจ๏Šจ๏Šจd.

  • A ๐‘ฅ 5 + 4 ๐‘ฅ 3 + 4 ๐‘ฅ + ๏Šซ ๏Šฉ C
  • B ๐‘ฅ 6 + ๐‘ฅ + 2 ๐‘ฅ + ๏Šญ ๏Šซ ๏Šฉ C
  • C 7 ๐‘ฅ + 2 0 ๐‘ฅ + 1 2 ๐‘ฅ + ๏Šญ ๏Šซ ๏Šฉ C
  • D ๐‘ฅ 7 + 4 ๐‘ฅ 5 + 4 ๐‘ฅ 3 + ๏Šญ ๏Šซ ๏Šฉ C

Q19:

Determine ๏„ธ๏€ปโˆ’4โˆš๐‘ฅ+8๏‡โˆš๐‘ฅ๐‘ฅ๏Žค๏Žค๏Šฏ๏Šจd.

  • A โˆ’ 5 ๐‘ฅ 4 + 4 0 ๐‘ฅ 7 + ๏Ž  ๏Žฅ ๏Žค ๏Žฆ ๏Žค C
  • B โˆ’ 6 4 ๐‘ฅ 5 + 5 6 ๐‘ฅ 5 + ๏Ž  ๏Žฅ ๏Žค ๏Žฆ ๏Žค C
  • C โˆ’ 7 2 ๐‘ฅ 7 3 + 1 6 ๐‘ฅ 7 + ๏Žฆ ๏Žข ๏Ž  ๏Žง ๏Žฆ ๏Žก C
  • D โˆ’ 2 0 ๐‘ฅ 1 1 + 2 0 ๐‘ฅ + ๏Ž  ๏Žฅ ๏Žค ๏Žฆ ๏Žค C

Q20:

Determine ๏„ธ๏€ฟ9โˆš๐‘ฅ+2๐‘ฅโˆ’1โˆš๐‘ฅ๏‹๐‘ฅd.

  • A 1 2 ๏€ป โˆ’ 2 โˆš ๐‘ฅ + ๐‘ฅ + 6 โˆš ๐‘ฅ ๏‡ + ๏Šจ ๏Šฉ ๏Šจ C
  • B โˆ’ โˆš ๐‘ฅ + 2 ๐‘ฅ + 9 โˆš ๐‘ฅ + ๏Šจ ๏Šฉ C
  • C โˆ’ 2 โˆš ๐‘ฅ + ๐‘ฅ + 6 โˆš ๐‘ฅ + ๏Šจ ๏Šฉ C
  • D 8 โˆš ๐‘ฅ + ๐‘ฅ + ๏Šจ C

Q21:

Determine ๏„ธ๏€ป3โˆš๐‘ฅ+1๏‡๐‘ฅ๏Žข๏Šจ๏Šจd.

  • A 1 0 ๐‘ฅ + 3 6 ๐‘ฅ + ๐‘ฅ + ๏Žค ๏Žก ๏Šช C
  • B 1 2 ๐‘ฅ 5 + 9 ๐‘ฅ 4 + ๐‘ฅ + ๏Žค ๏Žก ๏Šช C
  • C 4 ๐‘ฅ + 3 ๐‘ฅ + ๐‘ฅ + ๏Žค ๏Žก ๏Šช C
  • D 2 7 ๐‘ฅ 7 + 1 8 ๐‘ฅ 5 + ๐‘ฅ + ๏Žฆ ๏Žข ๏Žค ๏Žข C

Q22:

Determine ๏„ธ8โˆš๐‘ฅ๐‘ฅ๏Žค๏Šฌd.

  • A 8 ๐‘ฅ + ๏Šฑ ๏Ž  ๏Žค C
  • B โˆ’ 4 0 1 1 ๐‘ฅ + ๏Šฑ ๏Ž  ๏Ž  ๏Žค C
  • C โˆ’ 8 5 ๐‘ฅ + ๏Šฑ ๏Ž  ๏Žค C
  • D โˆ’ 2 0 3 ๐‘ฅ + ๏Šฑ ๏Ž  ๏Žค C
  • E โˆ’ 4 0 ๐‘ฅ + ๏Šฑ ๏Ž  ๏Žค C

Q23:

Determine ๏„ธโˆš๐‘ฆโˆš๐‘ฆ๐‘ฆ๏Žค๏Žข๏Šจd.

  • A 1 5 ๐‘ฆ + ๏Ž  ๏Žฅ ๏Ž  ๏Žค C
  • B 1 6 ๐‘ฆ 1 5 + ๏Ž  ๏Žฅ ๏Ž  ๏Žค C
  • C 1 5 ๐‘ฆ 1 6 + ๏Ž  ๏Žฅ ๏Ž  ๏Žค C
  • D โˆ’ 1 5 1 4 ๐‘ฆ + ๏Ž  ๏Žฃ ๏Ž  ๏Žค C

Q24:

Determine ๏„ธ๏€นโˆ’7๐‘ฅโˆ’5๏…๏€นโˆ’๐‘ฅ+1๏…๐‘ฅ๏Šจ๏Šฉd.

  • A 7 ๐‘ฅ 6 + 5 ๐‘ฅ 4 โˆ’ 7 ๐‘ฅ 3 โˆ’ 5 ๐‘ฅ + ๏Šฌ ๏Šช ๏Šฉ C
  • B 4 2 ๐‘ฅ + 2 0 ๐‘ฅ โˆ’ 2 1 ๐‘ฅ โˆ’ 5 ๐‘ฅ + ๏Šฌ ๏Šช ๏Šฉ C
  • C 7 ๐‘ฅ 4 + 5 ๐‘ฅ 2 โˆ’ 7 ๐‘ฅ + ๏Šช ๏Šจ C
  • D 7 ๐‘ฅ 5 + 5 ๐‘ฅ 3 โˆ’ 7 ๐‘ฅ 2 โˆ’ 5 ๐‘ฅ + ๏Šฌ ๏Šช ๏Šฉ C

Q25:

Determine ๏„ธ๐‘ฅ+216๐‘ฅโˆ’6๐‘ฅ+36๐‘ฅ๏Šฉ๏Šจd.

  • A ๐‘ฅ 3 โˆ’ 3 ๐‘ฅ + 3 6 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • B ๐‘ฅ 2 โˆ’ 6 ๐‘ฅ + ๏Šจ C
  • C ๐‘ฅ 4 โˆ’ 2 1 6 ๐‘ฅ + ๏Šช C
  • D ๐‘ฅ 2 + 6 ๐‘ฅ + ๏Šจ C

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