August 10, 2021
Let's learn about the rules to intergration in A-Level Maths!
Power Rule
Example: What is ∫x3 dx ?
The question is asking "what is the integral of x3 ?"
We can use the Power Rule, where n=3:
Multiplication by constant
Example: What is ∫6x2 dx ?
We can move the 6 outside the integral:
Trigonometry (x in radians)
Example: what is the integral of sin(x) ?
From the table above it is listed as being −cos(x) + C
It is written as:
Sum Rule
Example:
What is ∫(cos x + x) dx ?
Use the Sum Rule:
Reciprocal rule
Integration by Parts
∫u v dx = u∫v dx −∫u' (∫v dx) dx
- u is the function u(x)
- v is the function v(x)
- u' is the derivative of the function u(x)
Exponential rule
Integration by Substitution
Note that we have g(x) and its derivative g'(x)
Example:
∫cos(x2) 2x dx
dx2/dx = 2x which cancels out the 2x here.
So ∫cos(x2) 2x dx = sin(x2) + C
Drafted by Eunice (Maths)
References:
https://www.mathsisfun.com/calculus/integration-by-parts.html
https://www.mathsisfun.com/calculus/integration-rules.html