What is the fundamental theorem of calculus?
- The Theorem states that integration is the inverse process of differentiation (see Powers of x)
- This form of the Theorem relates to Indefinite Integration
- An alternative version of the Fundamental Theorem of Calculus involves Definite Integration
What is “+c” (plus c)?
- When differentiating y, constant terms ‘disappear’
- for constants y = c, dy/dx = 0
- graphs of constants are horizontal lines and so have gradient (dy/dx) 0
- Integrating dy/dx, to get y, cannot determine the constant
- To acknowledge this constant, “+ c” is used
- c is called the constant of integration
Notation
- If it has more than one term the function to be integrated(called the integrand) should be in brackets
- “Integrate” -– “all of (…)” -– “with respect to x”
- dx means integrate with respect to x, any other letter is treated like a number (ie like a constant)
Worked Example
