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AQA A Level Maths: Pure復(fù)習(xí)筆記8.1.4 Area Under a Curve

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月9日 上午10:48

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

8.1.4-Notes-fig1

How do I find the area under a curve?

8.1.4-Notes-fig2

  • The value from?definite?integration?is equal to the “area under a curve”8.1.4-Notes-fig3

What if I am not told the limits?

8.1.4-Notes-fig4

  • ?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

8.1.4-Notes-fig5

Negative areas

8.1.4-Notes-fig6

  • ?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

8.1.4-Notes-fig7

What if the area is made up of more than one section?

8.1.4-Notes-fig8

  • 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

    8.1.4-Notes-fig9

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

8.1.4-Example-fig1

 

 

 

 

 

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