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:
“For the most part, punishment makes men harder and colder; it concentrates; it sharpens the sense of estrangement; it strengthens the power of resistance.”
—Friedrich Nietzsche (1844–1900)
“The world is filled with the proverbs and acts and winkings of a base prudence, which is a devotion to matter, as if we possessed no other faculties than the palate, the nose, the touch, the eye and ear; a prudence which adores the Rule of Three, which never subscribes, which never gives, which seldom lends, and asks but one question of any project,—Will it bake bread?”
—Ralph Waldo Emerson (1803–1882)