# Worksheet: The Fundamental Theorem of Calculus: Evaluating Definite Integrals

In this worksheet, we will practice using the fundamental theorem of calculus to evaluate definite integrals.

Q1:

Evaluate .

Q2:

Evaluate .

• A
• B
• C
• D
• E

Q3:

Evaluate .

Q4:

Evaluate .

• A
• B
• C
• D0
• E

Q5:

Determine .

Q6:

Determine .

• A486
• B
• C54
• D

Q7:

Let . Evaluate the definite integral of from to .

Q8:

Evaluate .

• A
• B
• C
• D
• E6

Q9:

Let Determine .

Q10:

Determine .

• A
• B
• C
• D
• E

Q11:

Determine .

• A
• B
• C
• D

Q12:

Evaluate .

• A
• B
• C
• D
• E

Q13:

Evaluate .

• A6
• B
• C
• D
• E

Q14:

Evaluate .

• A
• B0
• C2
• D
• E

Q15:

Determine .

• A
• B
• C
• D

Q16:

If is the rate of growth of a child in grams per week, what does represent?

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

Q17:

Evaluate .

• A
• B
• C
• D54
• E

Q18:

Determine .

• A
• B
• C
• D

Q19:

If oil leaks from a tank at a rate of gallons per minute at time , which of the following does represent?

• AThe number of gallons of oil left in the tank after 120 minutes
• BThe number of gallons of oil leaked between the and minutes
• CThe number of gallons of oil left in the tank after 20 minutes
• DThe number of gallons of oil left in the tank after 70 minutes
• EThe number of gallons of oil leaked during the last minute

Q20:

Evaluate .

• A
• B
• C192
• D
• E

Q21:

Evaluate .

• A
• B
• C
• D
• E

Q22:

A honeybee population starts with 100 bees and increases at a rate of bees per week. What does represent?

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

Q23:

Evaluate .

• A
• B342
• C
• D

Q24:

Determine .

• A
• B
• C
• D

Q25:

If , determine .