Atividade: Integração de Funções Exponenciais

Nesta atividade, nós vamos praticar calcular integrais definidos e indefinidos de funções exponenciais utilizando diferentes técnicas.

Q1:

Determine ๏„ธ ๏€น 2 ๐‘’ โˆ’ ๐‘ฅ ๏… ๐‘ฅ ๏Šง ๏Šฆ ๏Šฏ ๏— d .

  • A 2 ๐‘’ โˆ’ 5 2 ๏Šฏ
  • B 2 ๐‘’ 9 โˆ’ 1 1 9 ๏Šฏ
  • C 2 ๐‘’ โˆ’ 3 ๏Šฏ
  • D 2 ๐‘’ 9 โˆ’ 1 3 1 8 ๏Šฏ

Q2:

Determine ๏„ธ โˆ’ 5 โˆš 5 ๐‘’ ๐‘› ๏Šฑ โˆš ๏Šซ ๏Š d .

  • A โˆ’ 5 โˆš 5 ๐‘’ + ๏Šฑ โˆš ๏Šซ ๏Š C
  • B 2 5 ๐‘’ + ๏Šฑ โˆš ๏Šซ ๏Š C
  • C 5 ๐‘’ + ๏Š C
  • D 5 ๐‘’ + ๏Šฑ โˆš ๏Šซ ๏Š C

Q3:

Calcule ๏„ธ ( ๐‘ฅ + 2 ๐‘’ ) ๐‘ฅ ๏Šง ๏Šฆ ๏Œพ ๏— d .

  • A โˆ’ 2 + 1 ๐‘’ + 2 ๐‘’
  • B โˆ’ 1 + 2 ๐‘’
  • C โˆ’ 2 ๐‘’ + 1
  • D โˆ’ 2 + 1 1 + ๐‘’ + 2 ๐‘’
  • E โˆ’ 2 ๐‘’ โˆ’ 1 1 + ๐‘’ + 2

Q4:

Determine ๏„ธ 8 ๐‘’ โˆ’ ๐‘’ + 9 7 ๐‘’ ๐‘ฅ ๏Šฉ ๏— ๏Šจ ๏— ๏— d .

  • A 1 6 7 ๐‘’ โˆ’ ๐‘’ 7 โˆ’ 9 7 ๐‘’ + ๏Šจ ๏— ๏— ๏Šฑ ๏— C
  • B 8 7 ๐‘’ โˆ’ ๐‘’ 7 + 9 7 ๐‘’ + ๏Šจ ๏— ๏— ๏Šฑ ๏— C
  • C 4 7 ๐‘’ โˆ’ ๐‘’ 7 + 9 7 ๐‘’ + ๏Šจ ๏— ๏— ๏Šฑ ๏— C
  • D 4 7 ๐‘’ โˆ’ ๐‘’ 7 โˆ’ 9 7 ๐‘’ + ๏Šจ ๏— ๏— ๏Šฑ ๏— C

Q5:

Dado que ๐‘“ โ€ฒ โ€ฒ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + 2 ๐‘ฅ ๏Šช ๏— ๏Šซ , encontre ๐‘“ ( ๐‘ฅ ) .

  • A ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 4 ๐‘’ + ๐‘ฅ 3 + ๏Šช ๏— ๏Šฌ C
  • B ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + 2 ๐‘ฅ + ๏Šช ๏— ๏Šฌ C
  • C ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + 2 ๐‘ฅ + ๐‘ฅ + ๏Šช ๏— ๏Šญ C D
  • D ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 1 6 ๐‘’ + ๐‘ฅ 2 1 + ๐‘ฅ + ๏Šช ๏— ๏Šญ C D
  • E ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + ๐‘ฅ 2 1 + ๐‘ฅ + ๏Šฌ ๏— ๏Šญ C D

Q6:

Determine ๏„ธ ๏€น 3 ๐‘’ + 8 ๐‘ฅ ๏… ๐‘ฅ ๏Šฉ ๏Šฆ ๏Šซ ๏— d .

  • A 3 ๐‘’ + 3 3 ๏Šง ๏Šซ
  • B 3 ๐‘’ 5 + 3 5 7 5 ๏Šง ๏Šซ
  • C 3 ๐‘’ + 6 9 ๏Šง ๏Šซ
  • D 3 ๐‘’ 5 + 1 7 7 5 ๏Šง ๏Šซ

Q7:

Determine ๏„ธ โˆ’ 4 9 7 ๐‘ฅ + 5 ๐‘ฅ d .

  • A โˆ’ 7 | 7 ๐‘ฅ + 5 | + l n C
  • B โˆ’ 4 9 ๐‘ฅ 5 โˆ’ 7 | ๐‘ฅ | + l n C
  • C โˆ’ 4 9 ๐‘ฅ 5 โˆ’ 4 9 | ๐‘ฅ | + l n C
  • D โˆ’ 7 | 7 ๐‘ฅ + 5 | + l n C

Q8:

Determine ๏„ธ โˆ’ 2 3 ๐‘ฅ 7 ๐‘ฅ l n d .

  • A 2 3 7 | ๐‘ฅ | + l n l n C
  • B โˆ’ 2 3 7 | ๐‘ฅ | + l n l n C
  • C 2 3 7 | ๐‘ฅ | + l n l n C
  • D โˆ’ 2 3 7 | ๐‘ฅ | + l n l n C

Q9:

Determine ๏„ธ 4 ๐œ‹ ๐‘’ ๐‘ฅ ๏Šฉ ๏— d .

  • A 4 ๐œ‹ 3 ๐‘’ + ๏Šฉ ๏— ๏Šฑ ๏Šง C
  • B 4 ๐œ‹ ๐‘’ + ๏Šฉ ๏— C
  • C 4 ๐œ‹ 3 ๐‘’ + ๏Šฉ ๏— ๏Šฐ ๏Šง C
  • D 4 ๐œ‹ 3 ๐‘’ + ๏Šฉ ๏— C

Q10:

Determine ๏„ธ ( โˆ’ 2 ๐‘ฅ โˆ’ 5 ) ๐‘ฅ ๐‘ฅ ๏Šจ d .

  • A 4 ๐‘ฅ + 2 0 ๐‘ฅ + 2 5 | ๐‘ฅ | + ๏Šจ l n C
  • B 2 ๐‘ฅ + 2 0 ๐‘ฅ + 2 5 | ๐‘ฅ | + ๏Šจ l n C
  • C 4 ๐‘ฅ + 2 0 ๐‘ฅ + 2 5 | ๐‘ฅ | + ๏Šจ l n C
  • D 2 ๐‘ฅ + 2 0 ๐‘ฅ + 2 5 | ๐‘ฅ | + ๏Šจ l n C

Q11:

Determine ๏„ธ ๏€ผ 8 ๐‘ฅ + 4 ๐‘ฅ ๏ˆ ๐‘ฅ ๏Šฏ d .

  • A 8 ๐‘ฅ + 4 | ๐‘ฅ | + ๏Šง ๏Šฆ l n C
  • B 4 ๐‘ฅ 5 + 4 | ๐‘ฅ | + ๏Šง ๏Šฆ l n C
  • C 8 ๐‘ฅ + 4 | ๐‘ฅ | + ๏Šง ๏Šฆ l n C
  • D 4 ๐‘ฅ 5 + 4 | ๐‘ฅ | + ๏Šง ๏Šฆ l n C

Q12:

Determine ๏„ธ ๏€ผ 9 ๐‘’ + 5 2 ๐‘’ ๏ˆ ๐‘ฅ ๏Šฌ ๏— ๏Šฑ ๏Šฌ ๏— ๏Šจ d .

  • A 3 4 ๐‘’ + 4 5 ๐‘ฅ โˆ’ 5 4 8 ๐‘’ + ๏Šง ๏Šจ ๏— ๏Šฑ ๏Šง ๏Šจ ๏— C
  • B 8 1 ๐‘’ + 4 5 ๐‘ฅ + 2 5 4 ๐‘’ + ๏Šง ๏Šจ ๏— ๏Šฑ ๏Šง ๏Šจ ๏— C
  • C 2 7 4 ๐‘’ + 4 5 ๐‘ฅ + 2 5 4 8 ๐‘’ + ๏Šง ๏Šจ ๏— ๏Šฑ ๏Šง ๏Šจ ๏— C
  • D 2 7 4 ๐‘’ + 4 5 ๐‘ฅ โˆ’ 2 5 4 8 ๐‘’ + ๏Šง ๏Šจ ๏— ๏Šฑ ๏Šง ๏Šจ ๏— C

Q13:

Determine ๏„ธ ๏€น 8 ๐‘ฅ + 7 ๐‘’ ๏… ๐‘ฅ ๏Šฉ ๏Œพ ๏Šฑ ๏Šฎ ๏— d .

  • A 8 ๐‘ฅ 3 ๐‘’ + 1 + 7 ๐‘’ + ๏Šฉ ๏Œพ ๏Šฐ ๏Šง ๏Šฑ ๏Šฎ ๏— C
  • B โˆ’ 7 8 ๐‘’ + 8 3 ๐‘’ ๐‘ฅ + ๏Šฑ ๏Šฎ ๏— ๏Šฉ ๏Œพ ๏Šฐ ๏Šง C
  • C โˆ’ 7 8 ๐‘’ + 8 3 ๐‘’ ๐‘ฅ + ๏Šฑ ๏Šฎ ๏— ๏Šฐ ๏Šง ๏Šฉ ๏Œพ ๏Šฐ ๏Šง C
  • D 8 ๐‘ฅ 3 ๐‘’ + 1 โˆ’ 7 8 ๐‘’ + ๏Šฉ ๏Œพ ๏Šฐ ๏Šง ๏Šฑ ๏Šฎ ๏— C

Q14:

Determine ๏„ธ 2 ๐‘ฅ ๏Šฏ ๏— d .

  • A 2 2 + ๏Šฏ ๏— l n C
  • B โˆ’ 2 9 2 + ๏Šฏ ๏— l n C
  • C 2 2 + ๏Šฏ ๏— l n C
  • D 2 9 2 + ๏Šฏ ๏— l n C

Q15:

Determine ๏„ธ โˆ’ 5 7 ๐‘’ ๐‘ฅ ๏Šฉ ๏— ๏Šฑ ๏Šซ d .

  • A โˆ’ 5 7 ๐‘’ + ๏Šฉ ๏— ๏Šฑ ๏Šช C
  • B โˆ’ 5 7 ๐‘’ + ๏Šฉ ๏— ๏Šฑ ๏Šซ C
  • C โˆ’ 1 5 7 ๐‘’ + ๏Šฉ ๏— ๏Šฑ ๏Šซ C
  • D โˆ’ 5 2 1 ๐‘’ + ๏Šฉ ๏— ๏Šฑ ๏Šซ C

Q16:

Determine ๏„ธ โˆ’ 6 ๐‘’ ๐‘ฆ ๏Šฆ ๏Ž• ๏Šง ๏˜ d .

  • A โˆ’ 6 ๐‘’ + ๏Šฆ ๏Ž• ๏Šง ๏˜ C
  • B โˆ’ 0 , 6 ๐‘’ + ๏Šฆ ๏Ž• ๏Šง ๏˜ C
  • C โˆ’ 6 0 ๐‘’ + ๏˜ C
  • D โˆ’ 6 0 ๐‘’ + ๏Šฆ ๏Ž• ๏Šง ๏˜ C

Q17:

Determine ๏„ธ 7 ๐‘ฅ โˆ’ 3 6 ๐‘ฅ ๐‘ฅ ๏Šจ d .

  • A 7 ๐‘ฅ 3 โˆ’ 1 2 | ๐‘ฅ | + ๏Šจ l n C
  • B 7 ๐‘ฅ 6 โˆ’ 1 2 | ๐‘ฅ | + ๏Šจ l n C
  • C 7 ๐‘ฅ 1 2 โˆ’ 1 2 | ๐‘ฅ | + ๏Šจ l n C
  • D 7 ๐‘ฅ 1 2 โˆ’ 1 2 | ๐‘ฅ | + ๏Šจ l n C

Q18:

Determine ๏„ธ ๏€พ 7 ๐‘’ ๐‘ฅ + 2 ๐‘ฅ ๐‘’ ๏Š ๐‘ฅ ๏Šช d .

  • A 7 ๐‘’ | ๐‘ฅ | + 8 ๐‘ฅ ๐‘’ + l n C ๏Šซ
  • B 7 ๐‘’ | ๐‘ฅ | + ๐‘ฅ 2 ๐‘’ + l n C ๏Šซ
  • C 7 ๐‘’ | ๐‘ฅ | + 2 ๐‘ฅ 5 ๐‘’ + l n C ๏Šซ
  • D 7 ๐‘’ | ๐‘ฅ | + 2 ๐‘ฅ 5 ๐‘’ + l n C ๏Šซ

Q19:

Determine ๏„ธ โˆ’ 2 7 ๐‘ฅ ๐‘ฅ d ..

  • A 2 7 | ๐‘ฅ | + l n C
  • B โˆ’ 2 7 | ๐‘ฅ | + l n C
  • C 2 7 | ๐‘ฅ | + l n C
  • D โˆ’ 2 7 | ๐‘ฅ | + l n C

Q20:

Determine a primitiva de ๐น ( ๐‘ฅ ) da funรงรฃo ๐‘“ , dado ๐‘“ ( ๐‘ฅ ) = 5 2 + 4 ๐‘ฅ .

  • A ๐น ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 2 + | ๐‘ฅ | + l n C
  • B ๐น ( ๐‘ฅ ) = โˆ’ 5 ๐‘ฅ + 4 | ๐‘ฅ | + l n C
  • C ๐น ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 2 + 4 | ๐‘ฅ | + l n C
  • D ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ 2 + 4 | ๐‘ฅ | + l n C
  • E ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ 2 + | ๐‘ฅ | + l n C

Q21:

Determinar a antiderivada mais geral da funรงรฃo ๐‘Ÿ ( ๐œƒ ) = โˆ’ 3 ๐‘’ + 2 ๐œƒ ๐œƒ ๏ผ t g s e c .

  • A ๐‘… ( ๐œƒ ) = ๐‘’ ( โˆ’ 3 ๐œƒ + 3 ) + 2 ๐œƒ + ๏ผ ๏Šฑ ๏Šง s e c C
  • B ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ ๐œƒ + 1 + 2 ๐œƒ + ๏ผ ๏Šฐ ๏Šง s e c C
  • C ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ + ๐œƒ ๐œƒ + ๏ผ ๏Šจ ๏Šจ t g s e c C
  • D ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ + 2 ๐œƒ + ๏ผ s e c C
  • E ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ ๐œƒ + 1 + ๐œƒ ๐œƒ + ๏ผ ๏Šฐ ๏Šง ๏Šจ ๏Šจ t g s e c C

Q22:

Determine ๏„ธ 5 4 ๐‘ฅ ๐‘ฅ l n d .

  • A 1 4 ( ๐‘ฅ + 5 ) + l n C
  • B l n l n C 5 | 4 ๐‘ฅ | +
  • C 1 4 5 ๐‘ฅ + l n C
  • D 1 4 5 | ๐‘ฅ | + l n l n C

Q23:

Determine ๏„ธ ๏€ฟ 3 โˆš ๐‘ฅ + 7 9 โˆš ๐‘ฅ ๏‹ ๐‘ฅ ๏Šจ d .

  • A 9 ๐‘ฅ + 1 4 ๐‘ฅ 3 + 4 9 8 1 | ๐‘ฅ | + ๏Šจ l n C
  • B 3 ๐‘ฅ 2 + 1 4 ๐‘ฅ 3 + 7 9 | ๐‘ฅ | + ๏Šจ l n C
  • C 9 ๐‘ฅ 2 + 7 ๐‘ฅ 3 + 4 9 8 1 | ๐‘ฅ | + ๏Šจ l n C
  • D 9 ๐‘ฅ 2 + 1 4 ๐‘ฅ 3 + 4 9 8 1 | ๐‘ฅ | + ๏Šจ l n C

Q24:

Determine ๏„ธ ๏€ผ 7 4 ๐‘ฅ โˆ’ 6 ๐‘’ ๏ˆ ๐‘ฅ ๏Šฑ ๏Šจ ๏— d .

  • A 7 4 | ๐‘ฅ | + 3 ๐‘’ + l n C ๏Šฑ ๏Šจ ๏—
  • B 7 4 | ๐‘ฅ | โˆ’ 6 ๐‘’ + l n C ๏Šฑ ๏Šจ ๏—
  • C 7 | 4 ๐‘ฅ | + 3 ๐‘’ + l n C ๏Šฑ ๏Šจ ๏—
  • D 7 4 | ๐‘ฅ | + 3 ๐‘’ + l n C ๏Šฑ ๏Šจ ๏—

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