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:
“I had some short struggle in my mind whether I should resign my lover or my liberty, but this lasted not long. I found myself as free as air and could not bear the thought of putting myself in any man’s power for life only from a present capricious inclination.”
—Sarah Fielding (1710–1768)
“If all political power be derived only from Adam, and be to descend only to his successive heirs, by the ordinance of God and divine institution, this is a right antecedent and paramount to all government; and therefore the positive laws of men cannot determine that, which is itself the foundation of all law and government, and is to receive its rule only from the law of God and nature.”
—John Locke (1632–1704)