some problems in integral calculus


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Definite Integrals
Definite Integrals - Differentiation deals with the rate of change while integration deals with the total change. The definite integrals are evaluated in problems relating to plane, areas, areas and volumes of solid of revolution etc. In this chapter, we conf..
Integration by Parts
In calculus, and more generally in mathematical analysis, integration by parts is a rule that transforms the integral of products of functions into other, possibly simpler, integrals. The rule arises from the product rule of differentiation. The f..
Integration by Substitution
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..
Integration by parts
In words: Integral of the product of two functions If the integrand is the product of two functions of different types then their order is determined by the word ILATE where I = Inverse trigonometric L = Logarithmic A = Algebraic, T = Trigonometric, E = Exponential In the integra..
Standard integrals
By method of completing squares ax 2 + bx + c is expressed as A 2 + X 2 or X 2 - A 2 and the integral reduces to which can be evaluated using the standard integrals..
Definite Integral
Let f (x) be a single valued continuous function defined in the interval [a,b] where b > 0 and let the interval [a,b] be divided into n equal parts each of length h, so that nh = b - a; then we define The method of evaluating by using the above definition is called integration from fir..
Integration by Substitution
Integration of the form - Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..
Integration of the form
Put g(x) = t Differentiating g(x) with respect to t, we have g'(x) dx = dt F(t) + C F(g(x)) +..
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