integration by substitution derivative

If u is a function of x, we can use the following formula to evaluate an integral. f dx = (f/(du/dx)) du Using the Formula Use of the formula is equivalent to the following procedure: 1. Write u as a function of x..

We know that one of the most important method of evaluation of indefinite integral is method of substitution. While using method of substitution to evaluate definite integrals, following steps are involved.We know that one of the most important method of eval..

We know that one of the most important method of evaluation of indefinite integral is method of substitution. While using method of substitution to evaluate definite integrals, following steps are involved. Working rule for Evaluating Definite ..

1. Both are operations on functions. 2. Both are linear. This is because of the following: (i) (ii) The constant can be taken outside the differential as well as integral sign as shown below: 3. We heve already seen that not all functions are differentiable. Similarly, all functions are n..

The reactions in which an atom or group of atoms in a molecule is replaced or substituted by different atoms or group of atoms are called substitution reaction. For example, In substitution reactions the hydrogen of the alkane molecule is replaced by another..

Aromatic compounds where the functional group is present in the sidechain of the ring are called sidechain substituted compounds. Sidechain substituted compounds are named as the phenyl derivatives of the corresponding aliphatic compound..

Electrophilic Substitution Reactions - All amino groups -NH 2 , -NHR, -NR 2 are most powerful activating groups in aromatic electrophilic substitution reactions are ortho and para directing. Aniline gets instantaneously brominated at all of the three O, p - positions to give a w..

Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent. Comparison between differentiation and integration: 1. The derivative of a function, when it exists is a unique function. The ..

Concentration dependence of rate is a differential equation (equation 8). It is tedious to determine the instantaneous rates from the slopes of the tangents for each value of t and this in turn makes the rate law determination difficult. To avoid this difficulty, the integrated form of th..

> The compound containing the two groups diagonally opposite to each other is called 'para': denoted as 'p-'. In the IUPAC system, the para position is designated as 1,4-. For example, the three xylenes are named as, o-xylene m-xylene p- xylene (1,2-dimethylbenzene) (1,3-dimethylbenzene) (1,3-dimet..