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:
“But it is impossible that the creative power should exclude itself. Into every intelligence there is a door which is never closed, through which the creator passes.”
—Ralph Waldo Emerson (1803–1882)
“A right rule for a club would be, Admit no man whose presence excludes any one topic. It requires people who are not surprised and shocked, who do and let do, and let be, who sink trifles, and know solid values, and who take a great deal for granted.”
—Ralph Waldo Emerson (1803–1882)