5.2a
General Power Rule:
Definition of the Natural Logarithmic Function:
The Log Rule for Integration:
Summary: In order to use the natural logarithmic function, one must turn a logarithmic function into an integral by using the substitution of u.
Real World: The natural logarithmic function for integration can be used in the real world to find out certain values as close as possible when using numbers not easy enough to work out mentally.
5.2b
Integral Functions
Summary: This section is an extension of 5.2a, however, these functions use the basic trigonometric functions. The process is the exact same, but it is good to know each function in order to substitute it into u.
Real World: The use of integrating trig functions can be useful in fields, especially engineering, to determine the amount of something there is or is needed.
Calculus Ants 