Atividade: Integração de Funções Exponenciais

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

Q1:

Determine ๏„ธ๏€น2๐‘’โˆ’๐‘ฅ๏…๐‘ฅ๏Šง๏Šฆ๏Šฏ๏—d.

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

Q2:

Determine ๏„ธโˆ’5โˆš5๐‘’๐‘›๏Šฑโˆš๏Šซ๏Šd.

  • A 2 5 ๐‘’ + ๏Šฑ โˆš ๏Šซ ๏Š C
  • B โˆ’ 5 โˆš 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+2๐‘’)๐‘ฅ๏Šง๏Šฆ๏Œพ๏—d.

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

Q4:

Determine ๏„ธ8๐‘’โˆ’๐‘’+97๐‘’๐‘ฅ๏Šฉ๏—๏Šจ๏—๏—d.

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

Q5:

Dado que ๐‘“โ€ฒโ€ฒ(๐‘ฅ)=โˆ’5๐‘’+2๐‘ฅ๏Šช๏—๏Šซ, encontre ๐‘“(๐‘ฅ).

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

Q6:

Determine ๏„ธ๏€น3๐‘’+8๐‘ฅ๏…๐‘ฅ๏Šฉ๏Šฆ๏Šซ๏—d.

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

Q7:

Determine ๏„ธโˆ’497๐‘ฅ+5๐‘ฅd.

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

Q8:

Determine ๏„ธโˆ’23๐‘ฅ7๐‘ฅlnd.

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

Q9:

Determine ๏„ธ4๐œ‹๐‘’๐‘ฅ๏Šฉ๏—d.

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

Q10:

Determine ๏„ธ(โˆ’2๐‘ฅโˆ’5)๐‘ฅ๐‘ฅ๏Šจd.

  • A 2 ๐‘ฅ + 2 0 ๐‘ฅ + 2 5 | ๐‘ฅ | + ๏Šจ l n C
  • B 4 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๏€ผ8๐‘ฅ+4๐‘ฅ๏ˆ๐‘ฅ๏Šฏd.

  • A 4 ๐‘ฅ 5 + 4 | ๐‘ฅ | + ๏Šง ๏Šฆ l n C
  • B 8 ๐‘ฅ + 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๏€ผ9๐‘’+52๐‘’๏ˆ๐‘ฅ๏Šฌ๏—๏Šฑ๏Šฌ๏—๏Šจd.

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

Q13:

Determine ๏„ธ๏€น8๐‘ฅ+7๐‘’๏…๐‘ฅ๏Šฉ๏Œพ๏Šฑ๏Šฎ๏—d.

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

Q14:

Determine๏„ธ2๐‘ฅ๏Šฏ๏—d.

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

Q15:

Determine ๏„ธโˆ’57๐‘’๐‘ฅ๏Šฉ๏—๏Šฑ๏Šซd.

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

Q16:

Determine ๏„ธโˆ’6๐‘’๐‘ฆ๏Šฆ๏Ž•๏Šง๏˜d.

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

Q17:

Determine ๏„ธ7๐‘ฅโˆ’36๐‘ฅ๐‘ฅ๏Šจd.

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

Q18:

Determine ๏„ธ๏€พ7๐‘’๐‘ฅ+2๐‘ฅ๐‘’๏Š๐‘ฅ๏Šชd.

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

Q19:

Determine ๏„ธโˆ’27๐‘ฅ๐‘ฅd..

  • 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)=52+4๐‘ฅ.

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

Q21:

Determinar a antiderivada mais geral da funรงรฃo ๐‘Ÿ(๐œƒ)=โˆ’3๐‘’+2๐œƒ๐œƒ๏ผtgsec.

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

Q22:

Determine ๏„ธ54๐‘ฅ๐‘ฅlnd.

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

Q23:

Determine ๏„ธ๏€ฟ3โˆš๐‘ฅ+79โˆš๐‘ฅ๏‹๐‘ฅ๏Šจd.

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

Q24:

Determine ๏„ธ๏€ผ74๐‘ฅโˆ’6๐‘’๏ˆ๐‘ฅ๏Šฑ๏Šจ๏—d.

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

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