CalculusAdditional / Further Maths

Area below the horizontal axis

Turn a negative signed integral into a positive area.

  • A curve below the horizontal axis gives a negative definite integral.
  • If on , the area is .
  • The final geometric area must be non-negative.

Example 1

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Example 2

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Your turn

Question 1

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Check answer
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Area is measured in square units.

Question 2

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Check answer
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Area is measured in square units.

Question 3

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Check answer
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Area is measured in square units.

Question 4

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Check answer
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Area is measured in square units.

Question 5

Find the shaded area.

The shaded region between the labelled curves and the stated limits.
Check answer
Integrate upper minus lower.Find an antiderivative.Substitute the limits.

Area is measured in square units.

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