Worksheet: Antiderivatives of Functions

In this worksheet, we will practice finding the antiderivative of a given function.

Q1:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ๐‘’ ๏Šจ .

  • A ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘’ ๐‘ฅ ๏Šจ
  • B ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘’ 3 + ๏Šฉ C
  • C ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘’ 3 ๏Šฉ
  • D ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘’ ๐‘ฅ + ๏Šจ C
  • E ๐น ( ๐‘ฅ ) = โˆ’ 6 ๐‘’ + ๏Šฉ C

Q2:

Find the antiderivative of the function ๐‘“ ( ๐‘ฅ ) = 2 ๐‘ฅ + 3 ๐‘ฅ + 3 2 .

  • A 2 ๐‘ฅ + 3 ๐‘ฅ + 3 ๐‘ฅ + 3 2 C
  • B ๐‘ฅ + 3 ๐‘ฅ + 3 ๐‘ฅ + 3 2 C
  • C 2 ๐‘ฅ 3 + 3 ๐‘ฅ + 3 ๐‘ฅ + 3 2 C
  • D 2 ๐‘ฅ 3 + 3 ๐‘ฅ 2 + 3 ๐‘ฅ + 3 2 C
  • E 2 ๐‘ฅ + 3 ๐‘ฅ 2 + 3 ๐‘ฅ + 3 2 C

Q3:

If ๐‘“ โ€ฒ โ€ฒ ( ๐‘ฅ ) = 3 ๐‘ฅ + 3 ๐‘ฅ + 5 ๐‘ฅ + 2 ๏Šซ ๏Šฉ , determine ๐‘“ ( ๐‘ฅ ) .

  • A ๐‘“ ( ๐‘ฅ ) = 3 ๐‘ฅ + 3 ๐‘ฅ + 5 ๐‘ฅ + 2 ๐‘ฅ + ๏Šญ ๏Šซ ๏Šฉ ๏Šจ C
  • B ๐‘“ ( ๐‘ฅ ) = ๐‘ฅ 2 + 3 ๐‘ฅ 4 + 5 ๐‘ฅ 2 + 2 ๐‘ฅ + ๏Šฌ ๏Šช ๏Šจ C
  • C ๐‘“ ( ๐‘ฅ ) = 3 ๐‘ฅ + 3 ๐‘ฅ + 5 ๐‘ฅ + 2 ๐‘ฅ + ๐‘ฅ + ๏Šญ ๏Šซ ๏Šฉ ๏Šจ C D
  • D ๐‘“ ( ๐‘ฅ ) = ๐‘ฅ 1 4 + 3 ๐‘ฅ 2 0 + 5 ๐‘ฅ 6 + ๐‘ฅ + ๐‘ฅ + ๏Šญ ๏Šซ ๏Šฉ ๏Šจ C D
  • E ๐‘“ ( ๐‘ฅ ) = 3 ๐‘ฅ 4 + 3 ๐‘ฅ 2 + ๏Šช ๏Šจ C

Q4:

Find the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ ๐‘ฅ ๏Šญ ๏Šซ ๏Šจ .

  • A ๐น ( ๐‘ฅ ) = ๐‘ฅ 8 + ๐‘ฅ 6 + ๐‘ฅ 3 + ๏Šฎ ๏Šฌ ๏Šฉ C
  • B ๐น ( ๐‘ฅ ) = 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ ๐‘ฅ + ๏Šฎ ๏Šฌ ๏Šฉ C
  • C ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ + ๐‘ฅ + ๏Šฎ ๏Šฌ ๏Šฉ C
  • D ๐น ( ๐‘ฅ ) = ๐‘ฅ 4 โˆ’ ๐‘ฅ 2 โˆ’ ๐‘ฅ 3 + ๏Šฎ ๏Šฌ ๏Šฉ C
  • E ๐น ( ๐‘ฅ ) = 1 6 ๐‘ฅ โˆ’ 1 8 ๐‘ฅ โˆ’ 3 ๐‘ฅ + ๏Šฎ ๏Šฌ ๏Šฉ C

Q5:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = 4 ๐‘ฅ ( โˆ’ ๐‘ฅ + 5 ) .

  • A ๐น ( ๐‘ฅ ) = โˆ’ 4 ๐‘ฅ 3 + 1 0 ๐‘ฅ + 2 C
  • B ๐น ( ๐‘ฅ ) = โˆ’ 4 ๐‘ฅ + 2 0 ๐‘ฅ + 3 2 C
  • C ๐น ( ๐‘ฅ ) = ๐‘ฅ โˆ’ 5 ๐‘ฅ + 3 2 C
  • D ๐น ( ๐‘ฅ ) = โˆ’ 4 ๐‘ฅ 3 + 1 0 ๐‘ฅ + 3 2 C
  • E ๐น ( ๐‘ฅ ) = โˆ’ 4 ๐‘ฅ โˆ’ 5 ๐‘ฅ + 2 C

Q6:

Determine the antiderivative ๐น of the function ๐‘“ ( ๐‘ฅ ) = 5 ๐‘ฅ + 4 ๐‘ฅ 4 3 where ๐น ( 1 ) = โˆ’ 2 .

  • A ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ + 1 7 5 4
  • B ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ + 4 ๐‘ฅ โˆ’ 1 1 5 4
  • C ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ + 4 ๐‘ฅ + 9 4 5 4
  • D ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ โˆ’ 4 5 4
  • E ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ โˆ’ 3 5 4

Q7:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ , given that 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

Q8:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = 6 ๐‘ฅ + 7 ๐‘ฅ ๏Ž  ๏Žค ๏Žก ๏Žค ๏Šฑ .

  • A ๐น ( ๐‘ฅ ) = ๐‘ฅ + 7 ๐‘ฅ 3 + ๏Žค ๏Žฅ ๏Žค ๏Žข C
  • B ๐น ( ๐‘ฅ ) = ๐‘ฅ + 7 ๐‘ฅ 3 + ๏Žฅ ๏Žค ๏Žข ๏Žค C
  • C ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ 6 + 5 ๐‘ฅ 3 + ๏Žฅ ๏Žค ๏Žข ๏Žค C
  • D ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ + 3 5 ๐‘ฅ 3 + ๏Žฅ ๏Žค ๏Žข ๏Žค C
  • E ๐น ( ๐‘ฅ ) = 3 6 ๐‘ฅ 5 + 2 1 ๐‘ฅ 5 + ๏Žค ๏Žฅ ๏Žค ๏Žข C

Q9:

Find the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = ( ๐‘ฅ โˆ’ 3 ) ๏Šจ .

  • A ๐น ( ๐‘ฅ ) = ๐‘ฅ 3 โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • B ๐น ( ๐‘ฅ ) = ๐‘ฅ โˆ’ 3 ๐‘ฅ + 9 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • C ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ + 9 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • D ๐น ( ๐‘ฅ ) = ๐‘ฅ 3 โˆ’ 3 ๐‘ฅ + 9 ๐‘ฅ + ๏Šฉ ๏Šจ C
  • E ๐น ( ๐‘ฅ ) = 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ โˆ’ 3 ๐‘ฅ + ๏Šฉ ๏Šจ C

Q10:

Find the most general antiderivative ๐บ ( ๐‘ก ) of the function ๐‘” ( ๐‘ก ) = โˆ’ 3 ๐‘ก + 5 ๐‘ก + 4 4 โˆš ๐‘ก ๏Šจ .

  • A ๐บ ( ๐‘ก ) = โˆ’ 3 ๐‘ก 4 โˆ’ 5 ๐‘ก 4 โˆ’ โˆš ๐‘ก + ๏Žค ๏Žก ๏Žข ๏Žก C
  • B ๐บ ( ๐‘ก ) = โˆ’ 1 5 ๐‘ก 8 โˆ’ 1 5 ๐‘ก 8 โˆ’ 2 โˆš ๐‘ก + ๏Žก ๏Žค ๏Žก ๏Žข C
  • C ๐บ ( ๐‘ก ) = โˆ’ 3 ๐‘ก 4 โˆ’ 5 ๐‘ก 4 โˆ’ โˆš ๐‘ก + ๏Žก ๏Žค ๏Žก ๏Žข C
  • D ๐บ ( ๐‘ก ) = โˆ’ 3 ๐‘ก 1 0 โˆ’ 5 ๐‘ก 6 โˆ’ 2 โˆš ๐‘ก + ๏Žค ๏Žก ๏Žข ๏Žก C
  • E ๐บ ( ๐‘ก ) = โˆ’ ๐‘ก 1 0 โˆ’ ๐‘ก 6 โˆ’ โˆš ๐‘ก 2 + ๏Žค ๏Žก ๏Žข ๏Žก C

Q11:

Find the most general antiderivative of the function ๐‘“ ( ๐‘ฅ ) = 4 ๐‘ฅ + 3 โˆ’ 2 3 โˆš ๐‘ฅ s i n .

  • A ๐น ( ๐‘ฅ ) = โˆ’ 2 โˆš ๐‘ฅ 3 + 3 ๐‘ฅ โˆ’ 4 ๐‘ฅ + c o s C
  • B ๐น ( ๐‘ฅ ) = โˆ’ 4 โˆš ๐‘ฅ 3 + 3 ๐‘ฅ + 4 ๐‘ฅ + c o s C
  • C ๐น ( ๐‘ฅ ) = โˆ’ 2 โˆš ๐‘ฅ 3 + 3 ๐‘ฅ + 4 ๐‘ฅ + c o s C
  • D ๐น ( ๐‘ฅ ) = โˆ’ 4 โˆš ๐‘ฅ 3 + 3 ๐‘ฅ โˆ’ 4 ๐‘ฅ + c o s C
  • E ๐น ( ๐‘ฅ ) = 4 โˆš ๐‘ฅ + 3 ๐‘ฅ โˆ’ 4 ๐‘ฅ + c o s C

Q12:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 โˆš ๐‘ฅ + 3 ๐‘ฅ โˆš ๐‘ฅ 3 2 .

  • A ๐น ( ๐‘ฅ ) = โˆ’ 3 ๐‘ฅ + 9 ๐‘ฅ 2 + 3 5 2 5 C
  • B ๐น ( ๐‘ฅ ) = โˆ’ 1 0 ๐‘ฅ 3 + 6 ๐‘ฅ 5 + 5 3 5 2 C
  • C ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ + 3 ๐‘ฅ + 5 3 5 2 C
  • D ๐น ( ๐‘ฅ ) = โˆ’ 6 ๐‘ฅ 5 + 6 ๐‘ฅ 5 + 5 3 5 2 C
  • E ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ + 3 ๐‘ฅ + 3 5 2 5 C

Q13:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = โˆš ๐‘ฅ + 5 โˆš ๐‘ฅ ๏Žข .

  • A ๐น ( ๐‘ฅ ) = 4 ๐‘ฅ 3 + 1 5 ๐‘ฅ 2 + ๏Žข ๏Žฃ ๏Žก ๏Žข C
  • B ๐น ( ๐‘ฅ ) = 4 ๐‘ฅ 3 + 1 5 ๐‘ฅ 2 + ๏Žฃ ๏Žข ๏Žข ๏Žก C
  • C ๐น ( ๐‘ฅ ) = ๐‘ฅ + 5 ๐‘ฅ + ๏Žฃ ๏Žข ๏Žข ๏Žก C
  • D ๐น ( ๐‘ฅ ) = 3 ๐‘ฅ 4 + 1 0 ๐‘ฅ 3 + ๏Žฃ ๏Žข ๏Žข ๏Žก C
  • E ๐น ( ๐‘ฅ ) = ๐‘ฅ + 5 ๐‘ฅ + ๏Žข ๏Žฃ ๏Žก ๏Žข C

Q14:

Find the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = 2 5 ๐‘ฅ + 2 9 5 ๐‘ฅ + 5 ๏Šจ ๏Šจ .

  • A ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ โˆ’ 4 ๐‘ฅ 5 + t a n C ๏Šฑ ๏Šง
  • B ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ โˆ’ 4 ๐‘ฅ + t a n C
  • C ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ + 4 ๐‘ฅ + t a n C
  • D ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ + 4 ๐‘ฅ 5 + t a n C ๏Šฑ ๏Šง
  • E ๐น ( ๐‘ฅ ) = 5 ๐‘ฅ + 4 ๐‘ฅ 5 + s i n C ๏Šฑ ๏Šง

Q15:

Find, if possible, an antiderivative ๐น of ๐‘“ ( ๐‘ฅ ) = 1 2 ๐‘ฅ โˆ’ 1 that satisfies the conditions ๐น ( 0 ) = 1 and ๐น ( 1 ) = โˆ’ 1 .

  • A ๐น ( ๐‘ฅ ) = โŽง โŽจ โŽฉ 1 2 ( 1 โˆ’ 2 ๐‘ฅ ) + 1 ๐‘ฅ < 1 2 , 1 2 ( 2 ๐‘ฅ โˆ’ 1 ) โˆ’ 1 ๐‘ฅ > 1 2 l n f o r l n f o r
  • BNo such antiderivative exists.

Q16:

What is the antiderivative ๐น of ๐‘“ ( ๐‘ฅ ) = โˆ’ 5 + ๏€น 1 + ๐‘ฅ ๏… 2 โˆ’ 1 that satisfies ๐น ( 1 ) = 0 ?

  • A ๐น ( ๐‘ฅ ) = โˆ’ 5 ๐‘ฅ + ๐‘ฅ + 1 t a n โˆ’ 1
  • B ๐น ( ๐‘ฅ ) = โˆ’ 5 ๐‘ฅ + ๐‘ฅ + ๐œ‹ 4 + 5 t a n โˆ’ 1
  • C ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ โˆ’ ๐œ‹ 4 + 5 t a n โˆ’ 1
  • D ๐น ( ๐‘ฅ ) = โˆ’ 5 ๐‘ฅ + ๐‘ฅ โˆ’ ๐œ‹ 4 + 5 t a n โˆ’ 1
  • E ๐น ( ๐‘ฅ ) = ๐‘ฅ + ๐‘ฅ + 1 t a n โˆ’ 1

Q17:

Determine the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ if ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ + ๐‘ฅ โˆ’ 2 ๐‘ฅ 2 ๐‘ฅ ๏Šช ๏Šฉ ๏Šฉ and ๐‘ฅ > 0 .

  • A ๐น ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 2 + ๐‘ฅ 2 โˆ’ 1 ๐‘ฅ + ๏Šจ C , ๐‘ฅ > 0
  • B ๐น ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ + ๐‘ฅ 2 + 1 ๐‘ฅ + ๏Šจ C , ๐‘ฅ > 0
  • C ๐น ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 2 + ๐‘ฅ 2 + 2 ๐‘ฅ + ๏Šจ C , ๐‘ฅ > 0
  • D ๐น ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 2 + ๐‘ฅ 2 + 1 ๐‘ฅ + ๏Šจ C , ๐‘ฅ > 0
  • E ๐น ( ๐‘ฅ ) = โˆ’ ๐‘ฅ + ๐‘ฅ 2 + 1 ๐‘ฅ + ๏Šจ C , ๐‘ฅ > 0

Q18:

By considering the product rule, find a function ๐‘“ so that ๐‘“ โ€ฒ ( ๐‘ฅ ) = ๐‘’ โˆš ๐‘ฅ + 2 ๐‘’ โˆš ๐‘ฅ ๐‘ฅ ๐‘ฅ .

  • A ๐‘“ ( ๐‘ฅ ) = โˆš 2 ๐‘ฅ ๐‘’ ๐‘ฅ
  • B ๐‘“ ( ๐‘ฅ ) = โˆš ๐‘ฅ ๐‘’ ๐‘ฅ
  • C ๐‘“ ( ๐‘ฅ ) = ๐‘’ โˆš ๐‘ฅ ๐‘ฅ
  • D ๐‘“ ( ๐‘ฅ ) = 2 โˆš ๐‘ฅ ๐‘’ ๐‘ฅ
  • E ๐‘“ ( ๐‘ฅ ) = 2 ๐‘’ โˆš ๐‘ฅ ๐‘ฅ

Q19:

Find the most general antiderivative ๐น ( ๐‘ฅ ) of the function ๐‘“ ( ๐‘ฅ ) = 4 ๐‘ฅ โˆ’ 2 .

  • A ๐น ( ๐‘ฅ ) = ๐‘ฅ 2 โˆ’ 2 ๐‘ฅ + ๏Šจ C
  • B ๐น ( ๐‘ฅ ) = 4 ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๏Šจ C
  • C ๐น ( ๐‘ฅ ) = ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๏Šจ C
  • D ๐น ( ๐‘ฅ ) = 2 ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๏Šจ C
  • E ๐น ( ๐‘ฅ ) = 8 ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๏Šจ C

Q20:

Determine the most general antiderivative of the function ๐‘Ÿ ( ๐œƒ ) = โˆ’ 3 ๐‘’ + 2 ๐œƒ ๐œƒ ๐œƒ t a n s e c .

  • A ๐‘… ( ๐œƒ ) = ๐‘’ ( โˆ’ 3 ๐œƒ + 3 ) + 2 ๐œƒ + ๐œƒ โˆ’ 1 s e c C
  • B ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ ๐œƒ + 1 + 2 ๐œƒ + ๐œƒ + 1 s e c C
  • C ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ + ๐œƒ ๐œƒ + ๐œƒ 2 2 t a n s e c C
  • D ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ + 2 ๐œƒ + ๐œƒ s e c C
  • E ๐‘… ( ๐œƒ ) = โˆ’ 3 ๐‘’ ๐œƒ + 1 + ๐œƒ ๐œƒ + ๐œƒ + 1 2 2 t a n s e c C

Q21:

Determine the family of functions ๐‘“ for which ๐‘“ ( ๐‘ก ) = 3 ๐‘ก โˆ’ 2 โ€ฒ โ€ฒ โ€ฒ s i n .

  • A ๐‘“ ( ๐‘ก ) = โˆ’ ๐‘ก 3 + 3 ๐‘ก + ๐‘ก + ๐‘ก 3 2 c o s C D
  • B ๐‘“ ( ๐‘ก ) = โˆ’ 2 ๐‘ก 3 + 3 ๐‘ก + ๐‘ก + ๐‘ก + 3 2 c o s C D E
  • C ๐‘“ ( ๐‘ก ) = โˆ’ ๐‘ก 3 โˆ’ 3 ๐‘ก + ๐‘ก + ๐‘ก + 3 2 c o s C D E
  • D ๐‘“ ( ๐‘ก ) = โˆ’ ๐‘ก 3 + 3 ๐‘ก + ๐‘ก + ๐‘ก + 3 2 c o s C D E
  • E ๐‘“ ( ๐‘ก ) = โˆ’ ๐‘ก 3 โˆ’ 3 ๐‘ก + ๐‘ก + ๐‘ก 3 2 c o s C D

Q22:

If the rate of change in the area ๐ด of a metallic plate with respect to time due to heating is given by the relation d d ๐ด ๐‘ก = 0 . 0 3 6 ๐‘ก + 0 . 0 3 8 ๐‘ก , 2 where the area ๐ด is in square metres, and the time ๐‘ก is in minutes, given that ๐ด = 6 7 m 2 when ๐‘ก = 8 m i n u t e s , find, correct to the nearest two decimal places, the area of the plate just before heating.

Q23:

The second derivative of a function is 6 ๐‘ฅ and the equation of the tangent to its graph at ( โˆ’ 2 , โˆ’ 4 ) is 6 ๐‘ฅ โˆ’ ๐‘ฆ + 8 = 0 . Find the equation of the curve.

  • A ๐‘ฆ = ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 4 ๏Šจ
  • B ๐‘ฆ = ๐‘ฅ โˆ’ 8 ๐‘ฅ โˆ’ 6 ๏Šฉ
  • C ๐‘ฆ = ๐‘ฅ + 1 8 ๐‘ฅ + 4 0 ๏Šจ
  • D ๐‘ฆ = ๐‘ฅ โˆ’ 6 ๐‘ฅ โˆ’ 8 ๏Šฉ
  • E ๐‘ฆ = ๐‘ฅ โˆ’ 8 ๏Šจ

Q24:

Suppose that d d s i n c o s ๐‘ฆ ๐‘ฅ = โˆ’ 9 2 ๐‘ฅ โˆ’ 3 5 ๐‘ฅ and ๐‘ฆ = 7 when ๐‘ฅ = ๐œ‹ 6 . Find ๐‘ฆ in terms of ๐‘ฅ .

  • A ๐‘ฆ = โˆ’ 9 2 2 ๐‘ฅ โˆ’ 3 5 5 ๐‘ฅ + 8 9 2 0 s i n c o s
  • B ๐‘ฆ = โˆ’ 9 2 ๐‘ฅ โˆ’ 3 5 ๐‘ฅ + 1 3 s i n c o s
  • C ๐‘ฆ = โˆ’ 3 5 2 ๐‘ฅ โˆ’ 9 2 5 ๐‘ฅ + 8 9 2 0 s i n c o s
  • D ๐‘ฆ = โˆ’ 3 5 5 ๐‘ฅ + 9 2 2 ๐‘ฅ + 1 0 1 2 0 s i n c o s
  • E ๐‘ฆ = 9 2 5 ๐‘ฅ + 3 5 2 ๐‘ฅ + 8 9 2 0 s i n c o s

Q25:

Find the function of the curve whose first derivative is and the function equals 7 when equals .

  • A
  • B
  • C
  • D

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.