Area Between Curve & y-axis (DP IB Applications & Interpretation (AI)): Revision Note
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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
Examiner Tips and Tricks
The integral area formula for area between a curve and the y-axis is given in the exam formula booklet.
STEP 1
If a diagram is not given, use a GDC to draw the graph of
(orif already given in that form)
If not identifiable from the question, use the graph to find the limitsand
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
Examiner Tips and Tricks
If a diagram is not provided, sketching one can really help in this sort of question. Your GDC can help with this.
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
Worked Example
Find the area enclosed by the curve with equation, the
-axis and the horizontal lines with equations
and
.

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