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Worksheet: Definite Integrals

Q1:

The graph of a function 𝑓 is shown. Which is the graph of an antiderivative of 𝑓 ?

  • A 𝑐
  • B π‘Ž
  • C 𝑏

Q2:

Determine ο„Έ ( 4 π‘₯ + 1 ) ( 2 π‘₯ βˆ’ 6 ) π‘₯ d .

  • A 8 π‘₯ + C
  • B 8 π‘₯ βˆ’ 2 2 π‘₯ βˆ’ 6 π‘₯ + 3 2 C
  • C 2 4 π‘₯ βˆ’ 4 4 π‘₯ βˆ’ 6 π‘₯ + 3 2 C
  • D 8 3 π‘₯ βˆ’ 1 1 π‘₯ βˆ’ 6 π‘₯ + 3 2 C
  • E 4 π‘₯ βˆ’ 2 2 π‘₯ βˆ’ 6 π‘₯ + 3 2 C

Q3:

If 𝑀 ( 𝑑 ) is the rate of growth of a child in grams per week, what does ο„Έ 𝑀 ( 𝑑 ) 𝑑 5 1 d represent?

  • AIt represents the child’s weight (in grams) at the age of 5 weeks.
  • BIt represents the child’s weight (in grams) at the age of 1 week.
  • CIt represents the increase in the child’s weight (in grams) during the last week.
  • DIt represents the net change in the child’s weight (in grams) between the ages of 1 and 5 weeks.
  • EIt represents the child’s weight (in grams) at the age of 3 weeks.

Q4:

Evaluate ο„Έ 4 βˆ’ 5 π‘₯ √ π‘₯ π‘₯ 4 1 2 d .

  • A βˆ’ 6
  • B βˆ’ 4 3 7 3
  • C 4 3 7 3
  • D βˆ’ 5 4
  • E54

Q5:

Determine ο„Έ 5 π‘₯ + 8 π‘₯ 7 π‘₯ π‘₯ 2 d .

  • A 8 7 π‘₯ + 5 1 4 + βˆ’ 1 C
  • B 5 7 π‘₯ + 8 7 π‘₯ + 2 C
  • C 1 0 7 π‘₯ + 8 7 π‘₯ + 2 C
  • D 5 1 4 π‘₯ + 8 7 π‘₯ + 2 C

Q6:

Let Determine ο„Έ 𝑓 ( π‘₯ ) π‘₯ 3 βˆ’ 1 d .

Q7:

If oil leaks from a tank at a rate of π‘Ÿ ( 𝑑 ) gallons per minute at time 𝑑 , which of the following does ο„Έ π‘Ÿ ( 𝑑 ) 𝑑      d represent?

  • Athe number of gallons of oil left in the tank after 20 minutes
  • Bthe number of gallons of oil left in the tank after 120 minutes
  • Cthe number of gallons of oil leaked during the last minute
  • Dthe number of gallons of oil leaked between the 20th and 1 2 0 t h minutes
  • Ethe number of gallons of oil left in the tank after 70 minutes

Q8:

Evaluate ο„Έ 4 𝑠 4 3 𝑠 d .

  • A 9 6 2 l o g
  • B192
  • C βˆ’ 1 9 2
  • D 9 6 2 l n
  • E βˆ’ 9 6 2 l n

Q9:

The figure shows the graph of the function ο„Έ 𝑓 ( 𝑑 ) 𝑑 . π‘₯ 0 d

Which of the following is the graph of 𝑦 = 𝑓 ( π‘₯ ) ?

  • A(c)
  • B(a)
  • C(d)
  • D(b)

Q10:

The figure shows the graph of the function ο„Έ 𝑓 ( 𝑑 ) 𝑑 . π‘₯ 0 d

Which of the following is the graph of 𝑦 = 𝑓 ( π‘₯ ) ?

  • A
  • B
  • C
  • D
  • Enone of these

Q11:

Evaluate ο„Έ ο„ž 3 𝑧 𝑧 1 8 1 6 d .

  • A 8 √ 3 + 6 √ 6
  • B βˆ’ 4 √ 3 + 3 √ 6
  • C βˆ’ 3 √ 6 + 4 √ 3
  • D βˆ’ 8 √ 3 + 6 √ 6
  • E βˆ’ 6 √ 6 + 8 √ 3

Q12:

A honeybee population starts with 100 bees and increases at a rate of π‘š ( 𝑑 ) bees per week. What does 1 0 0 + ο„Έ π‘š ( 𝑑 ) 𝑑 1 6 1 d represent?

  • AIt represents the net change in population between week 1 and week 8.
  • BIt represents the net change in population between week 1 and week 16.
  • CIt represents the total population in week 8.
  • DIt represents the total population in week 16.
  • EIt represents the total population in week 1.

Q13:

The figure shows the graph of the function ο„Έ 𝑓 ( 𝑑 ) 𝑑 . π‘₯ 0 d

Which of the following is the graph of 𝑦 = 𝑓 ( π‘₯ ) ?

  • A(c)
  • B(a)
  • C(b)
  • D(d)

Q14:

Determine ο„Έ 4 𝑒 𝑧 βˆ’ 6 𝑧 d .

  • A βˆ’ 2 3 𝑒 + βˆ’ 6 𝑧 βˆ’ 1 C
  • B 4 𝑒 + βˆ’ 6 𝑧 C
  • C βˆ’ 2 3 𝑒 + βˆ’ 6 𝑧 + 1 C
  • D βˆ’ 2 3 𝑒 + βˆ’ 6 𝑧 C

Q15:

If 𝑓 ( π‘₯ ) = 6 | π‘₯ | , determine ο„Έ 𝑓 ( π‘₯ ) π‘₯ 6 βˆ’ 6 d .

Q16:

Given the graph of 𝑓 below, if 𝐹 ( π‘₯ ) = ο„Έ 𝑓 ( 𝑑 ) 𝑑 π‘₯ 2 d , which of the following is the largest?

  • A 𝐹 ( 3 )
  • B 𝐹 ( 1 )
  • C 𝐹 ( 4 )
  • D 𝐹 ( 2 )
  • E 𝐹 ( 5 )

Q17:

Consider the integral ο„Έ 𝑒 βˆ’ 𝑒 𝑒 + 𝑒 π‘₯ 𝑏 π‘Ž π‘₯ βˆ’ π‘₯ π‘₯ βˆ’ π‘₯ d . Which of the following is a correct characterization of this integral?

  • AThe integral is undefined if π‘Ž < 0 , 𝑏 > 0 and | π‘Ž | β‰  | 𝑏 | .
  • BThe integral is undefined if π‘Ž < 0 and 𝑏 > 0 .
  • CThe integral is undefined only if π‘Ž = 0 or 𝑏 = 0 .
  • DThe integral is defined for all finite values of π‘Ž and 𝑏 .
  • EThe integral is undefined only if π‘Ž or 𝑏 is an integer multiple of πœ‹ .

Q18:

Determine ο„Έ ο€Ό βˆ’ 7 π‘₯ βˆ’ 4 7 8 π‘₯  π‘₯ s i n s i n d .

  • A 7 π‘₯ + 3 2 7 8 π‘₯ + c o s c o s C
  • B βˆ’ 7 π‘₯ βˆ’ 1 1 4 8 π‘₯ + c o s c o s C
  • C βˆ’ 7 π‘₯ βˆ’ 3 2 7 8 π‘₯ + c o s c o s C
  • D 7 π‘₯ + 1 1 4 8 π‘₯ + c o s c o s C

Q19:

Evaluate ο„Έ | π‘₯ βˆ’ 2 | π‘₯ 5 βˆ’ 4 d .

  • A39
  • B 2 9 2
  • C βˆ’ 2 7 2
  • D 4 5 2