Integrating (ax + b)ⁿ, exponentials and trigonometric functions
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 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
- The chain rule in reverse
- Powers of a linear bracket
Read the transcript of the teaching part
Last time
Before we start: last time, in Integration, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The chain rule in reverse
When you differentiated a function of a linear bracket, the chain rule multiplied by the inner derivative. Integration undoes this by dividing by it. So every integral in this lesson follows the same one line pattern: integrate as normal, then divide by the number in front of x.
Powers of a linear bracket
To integrate a x plus b, to the n: add one to the power, divide by the new power, and divide by a. For two x plus one, to the cube, the answer is two x plus one, to the fourth, over eight. The eight is four, from the new power, times two, from the inner derivative.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Integrating (ax + b)ⁿ, exponential and trigonometric functions.
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.