# Worksheet: Applications of Indefinite Integration

In this worksheet, we will practice using indefinite integration to express a function given its rate of change.

Q1:

The slope at the point on the graph of a function is . What is , given that ?

• A
• B
• C
• D

Q2:

The area of a lamina is changing at the rate cm2/s, starting from an area of 60 cm2. Give an exact expression for the area of the lamina after 30 seconds.

• A cm2
• B cm2
• C cm2
• D cm2

Q3:

A curve passes through and the tangent at its point has slope . What is the equation of the curve?

• A
• B
• C
• D

Q4:

The gradient of the tangent to a curve is . For , the curve has a local minimum value of . Find the equation of the curve.

• A
• B
• C
• D

Q5:

Find the equation of a curve which passes through the point and, for each point on the curve, the slope of the tangent at that point is .

• A
• B
• C
• D

Q6:

A curve passes through the point . The slope of its tangent at a point on the curve is given by . Find the equation of the tangent at the point when is equal to 1.

• A
• B
• C
• D

Q7:

The slope at the point on the graph of a function is . Find the equation of the curve if it contains the point .

• A
• B
• C
• D

Q8:

The slope at the point on the graph of a function is . Find the equation of the curve if it contains the point .

• A
• B
• C
• D

Q9:

The second derivative of a curve is . The curve passes through the point and the gradient of the tangent at this point is . Find the equation of the curve.

• A
• B
• C
• D

Q10:

Find the equation of the curve given the gradient of the tangent is and the curve passes through the origin.

• A
• B
• C
• D

Q11:

A curve passes through the points and . Find the equation of the curve given the gradient of the tangent to the curve equals .

• A
• B
• C
• D
• E

Q12:

The slope at the point on the graph of a function is . What is , given that ?

• A
• B
• C
• D

Q13:

Given that the slope at is and , determine .

• A
• B
• C
• D

Q14:

A curve passes through and the normal at its point has slope . What is the equation of the curve?

• A
• B
• C
• D

Q15:

The slope at the point on the graph of a function is . What is if we know that ?

• A
• B
• C
• D

Q16:

Find the equation of the curve given the gradient of the normal to the curve is and the curve passes through the point .

• A
• B
• C
• D
• E

Q17:

Find the equation of the curve that passes through the point given that the gradient of the tangent to the curve is .

• A
• B
• C
• D

Q18:

Find the local minimum value of a curve given that its gradient is and the local maximum value is 21.

Q19:

The gradient of the tangent to a curve is where the value of the local maximum is 9. Find the equation of the curve and the value of the local minimum if it exists.

• A ,
• B , 5
• C ,
• D , 9

Q20:

If the rate of change of the sales in a factory is inversely proportional to time in weeks, and the sales of the factory after 2 weeks and 4 weeks are 118 units and 343 units, respectively, determine the sales of the factory after 8 weeks.

Q21:

The slope at the point on the graph of a function is . Find the equation of the curve if it contains the point .

• A
• B
• C
• D
• E

Q22:

Find the equation of the curve given the slope of the tangent to the curve at its point is and it passes through the point .

• A
• B
• C
• D

Q23:

Find the equation of the curve given and the equation of the tangent to the curve at is .

• A
• B
• C
• D

Q24:

A curve passes through and the tangent at its point has slope . What is the equation of the curve?

• A
• B
• C
• D

Q25:

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 meters 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.