Power Rule
Historically the power rule was derived as the inverse of Cavalieri's quadrature formula which gave the area under for any integer . Nowadays the power rule is derived first and integration considered as its inverse.
For integers, the derivative of is that is,
The power rule for integration
for is then an easy consequence. One just needs to take the derivative of this equality and use the power rule and linearity of differentiation on the right-hand side.
Read more about this topic: Power Rule
Famous quotes containing the words power and/or rule:
“The power we exert over the future behavior of our children is enormous. Even after they have left home, even after we have left the world, there will always be part of us that will remain with them forever.”
—Neil Kurshan (20th century)
“To me the “female principle” is, or at least historically has been, basically anarchic. It values order without constraint, rule by custom not by force. It has been the male who enforces order, who constructs power structures, who makes, enforces, and breaks laws.”
—Ursula K. Le Guin (b. 1929)