# Worksheet: Antiderivatives of Functions

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

Q1:

Determine the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q2:

Find the antiderivative of the function .

• A
• B
• C
• D
• E

Q3:

If , determine .

• A
• B
• C
• D
• E

Q4:

Find the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q5:

Determine the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q6:

Determine the antiderivative of the function where .

• A
• B
• C
• D
• E

Q7:

Determine the most general antiderivative of the function , given that .

• A
• B
• C
• D
• E

Q8:

Determine the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q9:

Find the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q10:

Find the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q11:

Find the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q12:

Determine the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q13:

Determine the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q14:

Find the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q15:

Find, if possible, an antiderivative of that satisfies the conditions and .

• A
• BNo such antiderivative exists.

Q16:

What is the antiderivative of that satisfies ?

• A
• B
• C
• D
• E

Q17:

Determine the most general antiderivative of the function if and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q18:

By considering the product rule, find a function so that .

• A
• B
• C
• D
• E

Q19:

Find the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q20:

Determine the most general antiderivative of the function .

• A
• B
• C
• D
• E

Q21:

Determine the family of functions for which .

• A
• B
• C
• D
• E

Q22:

If the rate of change in the area of a metallic plate with respect to time due to heating is given by the relation where the area is in square metres, and the time is in minutes, given that when , find, correct to the nearest two decimal places, the area of the plate just before heating.

Q23:

The second derivative of a function is and the equation of the tangent to its graph at is . Find the equation of the curve.

• A
• B
• C
• D
• E

Q24:

Suppose that and when . Find in terms of .

• A
• B
• C
• D
• E

Q25:

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

• A
• B
• C
• D