# Lesson Worksheet: Applications of Indefinite Integration Mathematics

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 that passes through the point and is such that 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

This lesson includes 31 additional questions and 357 additional question variations for subscribers.