Definite integrals and plane areas
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Area under a curve
- Definite integral as an area
Read the transcript of the teaching part
Last time
Before we start: last time, in Integrating (ax + b)ⁿ, exponentials and trigonometric functions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Area under a curve
How much land is under a curved road bridge, or how much water in a curved dam? Cut the shape into thin strips. Each strip is almost a rectangle. Add up infinitely many infinitely thin strips, and you have an integral. Integration finds areas that formulas cannot.
Definite integral as an area
The area between a curve, the x axis, and the lines x equals a and x equals b is the integral of y from a to b. Integrate, then substitute the upper limit, then the lower limit, and subtract. The curve must be above the axis for the integral to be the area.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Definite integrals and plane areas.
The whole chapter: Integration.
Chapter 14: Differentiation and integration
- Differentiation: standard functions, chain, product and quotient rules 5 min
- Tangents and normals 5 min
- Stationary points and the derivative tests 5 min
- Practical maxima and minima 5 min
- Connected rates of change and small increments 5 min
- Integration: powers of x and the reverse of differentiation 5 min
- Integrating (ax + b)ⁿ, exponentials and trigonometric functions 5 min
- Definite integrals and plane areas 5 min
- Kinematics: displacement, velocity, acceleration and graphs 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.