AQA A Level Maths: Pure复习笔记8.1.4 Area Under a Curve
Area Under a Curve
What does area under a curve mean?
- The phrase “area under a curve” refers to the area bounded by …
- ... the?x-axis
- … the graph of?y = f(x)
- … the vertical line?x = a
- … the vertical line?x = b
How do I find the area under a curve?
- The value from?definite?integration?is equal to the “area under a curve”
What if I am not told the limits?
- ?If limits are not provided they will be the?x-axis intercepts
- Set?y = 0?and solve the equation to find the?x-axis intercepts
Negative areas
- ?If the area lies underneath the?x-axis the value of the integral will be negative
- An?area?cannot be negative, so take the?modulus?of the integral
What if the area is made up of more than one section?
- Be careful when one section is above and one section is below the?x-axis
- You will need a separate integral for each section, BUT...
- ...One section's integral will be?negative
- ...One section's integral will be?positive
- So you’ll need to take the?modulus?before adding to find the total area
Exam Tip
- Add information to any diagram provided in the question, as well as axes intercepts and values of limits.
- Mark and shade the area you’re trying to find, and if no diagram is provided,?sketch?one!
Worked Example
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