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 1 0 9 ๐‘ฅ d .

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

Q2:

Utilize a substituiรงรฃo adequada para determinar ๏„ธ ( 9 ๐‘ฅ + 7 ) ๐‘’ ๐‘ฅ ๏Šฏ ๏— ๏Šฐ ๏Šง ๏Šช ๏— ๏Žก d .

  • A ๐‘’ + ๏Šฏ ๏— ๏Šฐ ๏Šง ๏Šช ๏— ๏Žก C
  • B 2 ๐‘’ + ๏Šฏ ๏— ๏Šฐ ๏Šง ๏Šช ๏— ๏Žก C
  • C ๐‘’ + ๏Šง ๏Šฎ ๏— ๏Šฐ ๏Šจ ๏Šฎ ๏— ๏Žก C
  • D 1 2 ๐‘’ + ๏Šฏ ๏— ๏Šฐ ๏Šง ๏Šช ๏— ๏Žก C

Q3:

Determine ๏„ธ 7 3 ๐‘ฅ ๐‘ฅ c o s 3 ๐‘ฅ s e n d .

  • A 1 3 ๐‘’ + l n c o s 7 3 ๐‘ฅ C
  • B 7 3 7 + c o s 3 ๐‘ฅ l n C
  • C โˆ’ ๐‘’ 3 7 + c o s 3 ๐‘ฅ l n C
  • D โˆ’ 7 3 7 + c o s 3 ๐‘ฅ l n C

Q4:

Determine .

  • A
  • B
  • C
  • D

Q5:

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

Q6:

Determine ๏„ธ 9 ๐‘’ ( 7 + ๐‘’ ) ๐‘ฅ ๏Šฑ ๏— ๏Šฑ ๏— ๏Šจ d .

  • A โˆ’ 9 2 ( 7 + ๐‘’ ) + ๏Šฑ ๏— ๏Šฉ C
  • B โˆ’ 2 7 ( 7 + ๐‘’ ) + ๏Šฑ ๏— ๏Šฉ C
  • C 9 ( 7 + ๐‘’ ) + ๏Šฑ ๏— ๏Šฉ C
  • D โˆ’ 3 ( 7 + ๐‘’ ) + ๏Šฑ ๏— ๏Šฉ C

Q7:

Utilize a substituiรงรฃo apropriada para encontrar ๏„ธ 5 ๐‘’ ๐‘ฅ ๐‘ฅ โˆ’ 3 ๐‘ฅ 2 d .

  • A โˆ’ 3 0 ๐‘’ + โˆ’ 3 ๐‘ฅ 2 C
  • B โˆ’ 5 3 ๐‘’ + โˆ’ 3 ๐‘ฅ 2 C
  • C โˆ’ 1 5 ๐‘’ + โˆ’ 3 ๐‘ฅ 2 C
  • D โˆ’ 5 6 ๐‘’ + โˆ’ 3 ๐‘ฅ 2 C

Q8:

Determine ๏„ธ ๐‘ฅ + 9 ๐‘’ ๐‘ฅ ๐‘ฅ 2 ๐‘ฅ s e n c o s d .

  • A ๐‘ฅ + 9 ๐‘’ + 3 ๐‘ฅ s e n C
  • B ๐‘ฅ 2 โˆ’ 9 ๐‘’ + 3 ๐‘ฅ s e n C
  • C ๐‘ฅ โˆ’ 9 ๐‘’ + 3 ๐‘ฅ s e n C
  • D ๐‘ฅ 3 + 9 ๐‘’ + 3 ๐‘ฅ s e n C

Q9:

Determine ๏„ธ ๐‘’ ( 7 ๐‘ฅ โˆ’ 2 ) ๐‘ฅ 7 ๐‘ฅ โˆ’ 4 ๐‘ฅ โˆ’ 1 4 2 d .

  • A ๐‘’ + 7 ๐‘ฅ โˆ’ 4 ๐‘ฅ โˆ’ 1 4 2 C
  • B 2 ๐‘’ + 7 ๐‘ฅ โˆ’ 4 ๐‘ฅ โˆ’ 1 4 2 C
  • C โˆ’ ๐‘’ + 7 ๐‘ฅ โˆ’ 4 ๐‘ฅ โˆ’ 1 4 2 C
  • D 1 2 ๐‘’ + 7 ๐‘ฅ โˆ’ 4 ๐‘ฅ โˆ’ 1 4 2 C

Q10:

Determine ๏„ธ 8 ๐‘’ ๐‘’ ๐‘ฅ 7 ๐‘ฅ 7 ๐‘ฅ c o s d .

  • A 8 7 ๐‘’ ๐‘’ + โˆ’ 7 ๐‘ฅ 7 ๐‘ฅ s e n C
  • B โˆ’ 8 7 ๐‘’ + s e n C 7 ๐‘ฅ
  • C โˆ’ 8 7 ๐‘’ ๐‘’ + โˆ’ 7 ๐‘ฅ 7 ๐‘ฅ s e n C
  • D 8 7 ๐‘’ + s e n C 7 ๐‘ฅ

Q11:

Determine ๏„ธ ๐‘’ ๐‘’ โˆ’ 5 ๐‘ฅ 6 ๐‘ฅ 6 ๐‘ฅ d utilizando o mรฉtodo de substituiรงรฃo.

  • A 1 | ๐‘’ โˆ’ 5 | + l n C 6 ๐‘ฅ
  • B 1 6 | | ๐‘’ โˆ’ 5 | | + 6 ๐‘ฅ C
  • C l n C | | 6 ๐‘’ โˆ’ 5 | | + 6 ๐‘ฅ
  • D 1 6 | | ๐‘’ โˆ’ 5 | | + l n C 6 ๐‘ฅ
  • E 6 ๐‘’ + 6 ๐‘ฅ C

Q12:

Determine ๏„ธ โˆ’ 7 ๐‘’ โˆš โˆ’ 8 ๐‘’ + 3 ๐‘ฅ ๐‘ฅ ๐‘ฅ d .

  • A 7 4 โˆš โˆ’ 8 ๐‘’ + 3 + ๐‘ฅ C
  • B โˆ’ 1 4 โˆš โˆ’ 8 ๐‘’ + 3 + ๐‘ฅ C
  • C 7 8 โˆš โˆ’ 8 ๐‘’ + 3 + ๐‘ฅ C
  • D 7 4 โˆš โˆ’ 8 ๐‘’ + 3 + ๐‘ฅ C

Q13:

Determine ๏„ธ 8 ๐‘’ โˆ’ ๐‘’ + 9 7 ๐‘’ ๐‘ฅ 3 ๐‘ฅ 2 ๐‘ฅ ๐‘ฅ d .

  • A 1 6 7 ๐‘’ โˆ’ ๐‘’ 7 โˆ’ 9 7 ๐‘’ + 2 ๐‘ฅ ๐‘ฅ โˆ’ ๐‘ฅ C
  • B 8 7 ๐‘’ โˆ’ ๐‘’ 7 + 9 7 ๐‘’ + 2 ๐‘ฅ ๐‘ฅ โˆ’ ๐‘ฅ C
  • C 4 7 ๐‘’ โˆ’ ๐‘’ 7 + 9 7 ๐‘’ + 2 ๐‘ฅ ๐‘ฅ โˆ’ ๐‘ฅ C
  • D 4 7 ๐‘’ โˆ’ ๐‘’ 7 โˆ’ 9 7 ๐‘’ + 2 ๐‘ฅ ๐‘ฅ โˆ’ ๐‘ฅ C

Q14:

Determine ๏„ธ โˆ’ 1 โˆš 2 ๐‘ฅ ๐‘’ ๐‘ฅ โˆš 2 ๐‘ฅ d .

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

Q15:

Determine a funรงรฃo ๐‘“ se ๐‘“ โ€ฒ โ€ฒ ( ๐‘ฅ ) = โˆ’ 3 ๐‘’ + 4 ๐‘ฅ ๐‘ฅ s e n , ๐‘“ ( 0 ) = 4 e ๐‘“ ๏€ผ 3 ๐œ‹ 2 ๏ˆ = 0 .

  • A ๐‘“ ( ๐‘ฅ ) = โˆ’ 3 ๐‘’ โˆ’ 4 ๐‘ฅ + ๏ 6 ๐‘’ + 2 2 3 ๐œ‹ ๏ ๐‘ฅ + 7 ๐‘ฅ s e n 3 ๐œ‹ 2
  • B ๐‘“ ( ๐‘ฅ ) = โˆ’ 3 ๐‘’ โˆ’ 4 ๐‘ฅ + ๏ 6 ๐‘’ โˆ’ 2 2 3 ๐œ‹ ๏ ๐‘ฅ ๐‘ฅ c o s 3 ๐œ‹ 2
  • C ๐‘“ ( ๐‘ฅ ) = โˆ’ 3 ๐‘’ โˆ’ 4 ๐‘ฅ + ๏ 6 ๐‘’ + 2 2 3 ๐œ‹ ๏ ๐‘ฅ + 7 ๐‘ฅ c o s 3 ๐œ‹ 2
  • D ๐‘“ ( ๐‘ฅ ) = โˆ’ 3 ๐‘’ โˆ’ 4 ๐‘ฅ + ๏ 6 ๐‘’ โˆ’ 2 2 3 ๐œ‹ ๏ ๐‘ฅ + 7 ๐‘ฅ s e n 3 ๐œ‹ 2
  • E ๐‘“ ( ๐‘ฅ ) = ๐‘’ โˆ’ ๐‘ฅ + ๏ 6 ๐‘’ โˆ’ 2 2 3 ๐œ‹ ๏ ๐‘ฅ + 7 ๐‘ฅ s e n 3 ๐œ‹ 2

Q16:

Determine ๏„ธ 1 9 ๐‘’ + 1 9 ๐‘ฅ โˆ’ 2 0 ๐‘’ โˆ’ 2 0 ๐‘ฅ ๐‘ฅ ๐‘ฅ โˆ’ 1 ๐‘’ โˆ’ 1 ๐‘ฅ ๐‘’ d .

  • A โˆ’ 1 9 2 0 | ๐‘’ + ๐‘ฅ | + l n C ๐‘ฅ ๐‘’
  • B 1 9 2 0 ๐‘’ | ๐‘’ + ๐‘ฅ | + l n C ๐‘ฅ ๐‘’
  • C โˆ’ 1 9 2 0 ๐‘’ | | ๐‘’ + ๐‘ฅ | | + l n C ๐‘ฅ โˆ’ 1 ๐‘’ โˆ’ 1
  • D โˆ’ 1 9 2 0 ๐‘’ | ๐‘’ + ๐‘ฅ | + l n C ๐‘ฅ ๐‘’

Q17:

Determine ๏„ธ โˆ’ 9 ๐‘’ 7 ๐‘’ + 1 2 ๐‘ฅ ๐‘ฅ ๐‘ฅ d .

  • A โˆ’ 3 ๐‘’ 4 โˆ’ 9 ๐‘ฅ 7 + ๐‘ฅ C
  • B โˆ’ 6 3 | 7 ๐‘’ + 1 2 | + l n C ๐‘ฅ
  • C โˆ’ 9 7 | 7 ๐‘’ + 1 2 | + l n C ๐‘ฅ
  • D โˆ’ 9 7 | 7 ๐‘’ + 1 2 | + l n C ๐‘ฅ

Q18:

Uma xรญcara de chรก a 9 0 โˆ˜ C รฉ deixada em um quarto a 2 2 โˆ˜ C para esfriar a uma taxa de โˆ’ 1 0 , 2 ๐‘’ โˆ’ 0 , 1 5 ๐‘ก โˆ˜ per min. Qual รฉ a temperatura do chรก depois de 10 minutos para o grau mais prรณximo?

Q19:

Dado que ๐‘“ โ€ฒ โ€ฒ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + 2 ๐‘ฅ 4 ๐‘ฅ 5 , encontre ๐‘“ ( ๐‘ฅ ) .

  • A ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 4 ๐‘’ + ๐‘ฅ 3 + 4 ๐‘ฅ 6 C
  • B ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + 2 ๐‘ฅ + 4 ๐‘ฅ 6 C
  • C ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + 2 ๐‘ฅ + ๐‘ฅ + 4 ๐‘ฅ 7 C D
  • D ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 1 6 ๐‘’ + ๐‘ฅ 2 1 + ๐‘ฅ + 4 ๐‘ฅ 7 C D
  • E ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 ๐‘’ + ๐‘ฅ 2 1 + ๐‘ฅ + 6 ๐‘ฅ 7 C D

Q20:

Determine ๏„ธ ๏€น 3 ๐‘’ + 8 ๐‘ฅ ๏… ๐‘ฅ 3 0 5 ๐‘ฅ d .

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

Q21:

Determine ๏„ธ ๐‘’ ( 7 ๐‘ฅ + 1 ) ๐‘ฅ 7 ๐‘ฅ + 2 ๐‘ฅ โˆ’ 1 3 2 d .

  • A ๐‘’ + 7 ๐‘ฅ + 2 ๐‘ฅ โˆ’ 1 3 2 C
  • B 2 ๐‘’ + 7 ๐‘ฅ + 2 ๐‘ฅ โˆ’ 1 3 2 C
  • C โˆ’ ๐‘’ + 7 ๐‘ฅ + 2 ๐‘ฅ โˆ’ 1 3 2 C
  • D 1 2 ๐‘’ + 7 ๐‘ฅ + 2 ๐‘ฅ โˆ’ 1 3 2 C

Q22:

Utilize a substituiรงรฃo apropriada para encontrar ๏„ธ โˆ’ ๐‘’ ๐‘ฅ ๐‘ฅ 5 ๐‘ฅ 2 d .

  • A โˆ’ 1 0 ๐‘’ + 5 ๐‘ฅ 2 C
  • B โˆ’ ๐‘’ 5 + 5 ๐‘ฅ 2 C
  • C โˆ’ 5 ๐‘’ + 5 ๐‘ฅ 2 C
  • D โˆ’ ๐‘’ 1 0 + 5 ๐‘ฅ 2 C

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