Area between a line and a curve Revision Card

CalculusAdditional / Further Maths

Find intersection limits and integrate upper minus lower.

Solve the two equations together to find the intersection limits.
Between consecutive intersections, identify the upper and lower graphs.
. Split the interval if their order changes.

Example 1

Find the shaded area.

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Example 2

Find the shaded area.

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Your turn

Question 1

Find the shaded area.

Check answer

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Area is measured in square units.

Question 2

Find the shaded area.

Check answer

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Area is measured in square units.

Question 3

Find the shaded area.

Check answer

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Area is measured in square units.

Question 4

Find the shaded area.

Check answer

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Area is measured in square units.

Question 5

Find the shaded area.

Check answer

Set the functions equal: the intersections are

and

Integrate upper minus lower.

Find an antiderivative.

Substitute the limits.

Area is measured in square units.