Introduction to Integration

Introduction to Integrationvideo

Introduction to integration

What is integration?

• Integration is the opposite to differentiation

• Integration is the process of finding the expression of a function from an expression of the derivative (gradient function)

What is the fundamental theorem of calculus?

• The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation

  • This form of the Theorem relates to Indefinite Integration

  • An alternative version of the Fundamental Theorem of Calculus involves Definite Integration

What is the constant of integration (+c)?

•  When differentiating y, constant terms ‘disappear’

  • for constants y = c, $\frac{\mathrm{d}y}{\mathrm{d}x}=0$

  • graphs of constants are horizontal lines and so have gradient of 0

• Integrating $\frac{\mathrm{d}y}{\mathrm{d}x}$, to get y, cannot determine the constant

  • To acknowledge this constant, “+ c” is used

  • c is called the constant of integration

What is the notation for integration?

• An integral is normally written in the form

$\int f\left(x\right) \mathrm{d}x$ 

• the large operator $\int$ means “integrate”

  • “$\mathrm{d}x$” indicates which variable to integrate with respect to

  • $f\left(x\right)$ is the function to be integrated

• 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”