Area between two curves Revision Card

CalculusAdditional / Further Maths

Calculate the area enclosed by two curves.

Find the intersections by setting the two functions equal.
Integrate the upper function minus the lower function between adjacent intersection points.
For several enclosed regions, calculate each area separately and add them.

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.