Application To Indefinite Integrals
For example, if you know that the integral of exp(x) is exp(x) from calculus with exponentials and that the integral of cos(x) is sin(x) from calculus with trigonometry then:
Some other general results come from this rule. For example:
The proof above relied on the special case of the constant factor rule in integration with k=-1.
Thus, the sum rule might be written as:
Another basic application is that sigma and integral signs can be changed around. That is:
This is simply because:
Read more about this topic: Sum Rule In Integration
Famous quotes containing the words application to, application and/or indefinite:
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“The best political economy is the care and culture of men; for, in these crises, all are ruined except such as are proper individuals, capable of thought, and of new choice and the application of their talent to new labor.”
—Ralph Waldo Emerson (1803–1882)
“As they are not seen on their way down the streams, it is thought by fishermen that they never return, but waste away and die, clinging to rocks and stumps of trees for an indefinite period; a tragic feature in the scenery of the river bottoms worthy to be remembered with Shakespeare’s description of the sea-floor.”
—Henry David Thoreau (1817–1862)