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

• The function is normally given in the form

  • so will need rearranging into the form

•  and  may not be given directly and could involve the the -axis () and/or a root of (i.e. a point where the function intersects or touches the -axis)

  • 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 given 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

  • Your GDC may require to enter the function ‘’ as the variable (not ‘’)

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

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

Can there be 'negative integrals' for areas between a curve and the y-axis?

• 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

    • Your GDC will apply  automatically as long as you put the modulus symbol ( | ... | ) around