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:
“Preaching is the expression of the moral sentiment in application to the duties of life.”
—Ralph Waldo Emerson (1803–1882)
“I conceive that the leading characteristic of the nineteenth century has been the rapid growth of the scientific spirit, the consequent application of scientific methods of investigation to all the problems with which the human mind is occupied, and the correlative rejection of traditional beliefs which have proved their incompetence to bear such investigation.”
—Thomas Henry Huxley (1825–95)
“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)