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 bitterest creature under heaven is the wife who discovers that her husband’s bravery is only bravado, that his strength is only a uniform, that his power is but a gun in the hands of a fool.”
—Pearl S. Buck (1892–1973)
“After all, the practical reason why, when the power is once in the hands of the people, a majority are permitted, and for a long period continue, to rule is not because they are most likely to be in the right, nor because this seems fairest to the minority, but because they are physically the strongest. But a government in which the majority rule in all cases cannot be based on justice, even as far as men understand it.”
—Henry David Thoreau (1817–1862)