integration by parts vector

. Differentiation is a process involving limits, so is integration. 10. The process of differentiation and integration are inverses of each other. In the earlier section we have found the integral (antiderivative) of a function by inspection. For a given function f, it..

Let us consider the case of a projectile, which explodes in flight. The force of gravity continues to act on the total mass of the projectile, now scattered into fragments. The centre of mass of the fragments continues along the parabolic trajectory. It is the same, as was followed by the intact pr..

The plasmids are small, circular DNA molecules present in bacterial cells in addition to the chromosomal DNA. Genes from one organism may be added to the plasmids of a bacterium and transfer them to another. They retain their characters after combining with the DNA of another organisms. Not being ..

Question: What did Perkins decide to do to make up for the deficiencies with regard to the house and Katy? Answer: John Perkins was really a changed person now he realized the value of Katy in her absence. He sensed that Katy had become an integral part of his life..

When a light wave falls on a transparent solid, it causes the electrons in the solid to oscillate periodically in response to of the incident waves. Since these oscillating charges act coherently or cooperatively there is a lack of scattering of light. But in liquids or gases, due to a larger separ..

. It is high time man realises that he is an integral part of the environment. He should also realise that because he is at the pinnacle of evolution and has also more responsibility towards maintaining the environmen..

Summary - Electric charge is a basic property of all matter. Unlike charges attract, like charges repel. Conductor allow flow of electric charges through them while insulators don't. Electric charges have three basic properties (a) Additivity (b) Quantisation (c) Conservation Coulomb's law: the Ele..

During the course of study of Mathematics, we must have come across several parts of inverse operations like (addition, subtraction) (multiplication, division) (forming an equation whose roots are given - solving a given equation) and so on. In practical situations, we may be interested t..

In view of new discoveries about atoms, Dalton's atomic theory was modified as given below: Atom is no longer indivisible as it has a complex structure of sub atomic particles (electrons, protons and neutrons). Atoms of the same element may posses different relative masses (isotopes). Certain atoms..

Modern Atomic Theory - In view of new discoveries about atoms, Dalton's atomic theory was modified as given below: Atom is no longer indivisible as it has a complex structure of sub atomic particles (electrons, protons and neutrons). Atoms of the same element may posses different relative masses (i..