BASCAL

• the process of finding all antiderivatives of f(X) is called antidifferentiation.
• Antidifferentiation is also known as integration
• antiderivatives is also called as integrals of f
•  ∫ is called an integral sign and this ios used to dennote the integral function
• Integral of cosx=sinx + C
• integral of x^n/n+1 = (x^n+1)/(n+1)+C
• Integral of f(x) can be written as ∫ f(x) dx = F(x) + C
• Integration using substitution rule is also called as u-substitution or also known as the revese chain rule
• STEPS ON REVERSE CHAIN RULE:

  1. Find u and du
  2. Substitute
  3. Intergrate
  4. Final answer
• The du is the derivatives of u
• Definite integral is the difference between the value of the integral in the given function of f(x)
• The value of the given function can be upper value b and lower value a of the independent variable
• let f be a continuous function on the closed interval [a, b] which antiderivatives of F
• This  ∫ f(x) dx = F(x) + C is called indefinite integral
• what is the f(x) in ∫ f(x) dx = F(x) + C

  intergrand
• what is dx in ∫ f(x) dx = F(x) + C


  variable of integration
• what is F(x) in ∫ f(x) dx = F(x) + C?

  antiderivatives of f
• what is C in ∫ f(x) dx = F(x) + C?

  constant of function
• why is there an C in ∫ f(x) dx = F(x) + C?

  because C is definite
• Integration using substitution rule is a method to find an integral, but only can be set up in special case