Area Between Curve & y-axis (DP IB Applications & Interpretation (AI)): Revision Note

Area Between Curve & y-axis

What is meant by the area between a curve and the y-axis?

• The area referred to is the region bounded by

  • the graph of

  • the-axis

  • the horizontal line

  • the horizontal line

• The exact area can be found by evaluating a definite integral

How do I find the area between a curve and the y-axis?

• Use the formula

• This is given in the formula booklet

• The function is normally given in the form

  • so will need rearranging into the form

•  and  may not be given directly as could involve the the -axis () and/or a root of

  • use a GDC to plot the curve and find roots as necessary

STEP 1

If a diagram is not given, use a GDC to draw the graph of
(or if already in that form)
If not identifiable from the question, use the graph to find the limits  and 

STEP 2

If needed, rearrange into the form

STEP 3

Write down the definite integral needed to find the required area

Use a GDC to evaluate it

A GDC is likely to require the function written with ‘’ as the variable (not ‘’)

Remember to include the modulus ( | … | ) symbols around the function

Modulus may be called ‘Absolute value (Abs)’ on some GDCs

• In trickier problems some (or all) of the area may be 'negative'

  • this would be any area that is to the left of the -axis (negative  values)

  •  makes such areas 'positive' by reflecting them in the -axis

    • a GDC will apply  automatically as long as the modulus ( | ... | )symbols are included