Edexcel 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
转载自savemyexams
国际竞赛真题资料-点击免费领取！
早鸟钜惠！翰林2025暑期班课上线
美高学分项目重磅来袭！立即了解
