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[1] The velocity of detonation is an important indicator for overall energy and power of detonation, and in particular for the brisance or shattering effect of an explosive which is due to the detonation pressure.
2,4,6-Trinitrobenzoic acid is prepared by oxidation of 2,4,6-trinitrotoluene (TNT). It is formed by oxidation of TNT and nitric acid with chlorate [2] and with dichromate. [3] Upon heating, 2,4,6-trinitrobenzoic acid undergoes decarboxylation to give 1,3,5-trinitrobenzene. [4]
Trinitrotoluene (/ ˌ t r aɪ ˌ n aɪ t r oʊ ˈ t ɒ lj u iː n /), [5] [6] more commonly known as TNT (and more specifically 2,4,6-trinitrotoluene, and by its preferred IUPAC name 2-methyl-1,3,5-trinitrobenzene), [1] is a chemical compound with the formula C 6 H 2 (NO 2) 3 CH 3. TNT is occasionally used as a reagent in chemical synthesis ...
At this point we can either integrate directly, or we can first change the integrand to 2 cos 6x − 4 cos 4x + 2 cos 2x and continue from there. Either method gives Either method gives ∫ sin 2 x cos 4 x d x = − 1 24 sin 6 x + 1 8 sin 4 x − 1 8 sin 2 x + C . {\displaystyle \int \sin ^{2}x\cos 4x\,dx=-{\frac {1}{24 ...
In mathematics, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} is the area of the region in the xy -plane bounded by the graph of f , the x -axis, and the lines x = a and x = b , such that area above the x -axis adds to the total, and that below the x -axis subtracts from the total.
Integrands of the form x m (a + b x n + c x 2n) p when b 2 − 4 a c = 0 [ edit ] The resulting integrands are of the same form as the original integrand, so these reduction formulas can be repeatedly applied to drive the exponents m and p toward 0.
An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with volumes 1–3 listing integrals and series of elementary and special functions, volume 4–5 are tables of Laplace transforms).
The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by I n, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example I n-1 or I n-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction ...