Indefinite Integrals Summary
Summary - f(x) is called the integrand, F(x) is called the particular integral and C the constant of integration..
Summary - f(x) is called the integrand, F(x) is called the particular integral and C the constant of integration..Indefinite Integrals as Antiderivative
Let us define integral of a function in general as follows. Let F(x) be a function such that \ In general, integral of f(x) is F(x) + C Where C is called the constant of integration..
Let us define integral of a function in general as follows. Let F(x) be a function such that \ In general, integral of f(x) is F(x) + C Where C is called the constant of integration..Indefinite Integrals as Antiderivative (Contd...)
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 integral of a..
Second Fundamental Theorem of Integral Calculus
Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =..
Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =..Greatest Terms for Positive Integral Index
Working rules for finding the greatest term: Step 1: In (a + b) n , the constants a and b must be positive. Step 2: Write T r+1 and T r and find the value of T r+1 /T r . Step 3: Simplify the inequality (T r+1 /T r ) greater than or equal to 1 and find the..
If ∫3x2 + 6(x2 + 1)(x2 + 4) dx ..
If ∫ 3 x 2 + 6 ( x 2 + 1 ) ( x 2 + 4 ) d x = Ktan -1 ( m x c + x 2 ) + A , then find the values of K, m , c , where A is a constant of integration..
Note:
Where P and Q are functions of y only is a Leibnitz's linear differential equation which is linear in x and its solution is given by C is a constant of integration..
Where P and Q are functions of y only is a Leibnitz's linear differential equation which is linear in x and its solution is given by C is a constant of integration..Note:
(1) While integration by parts, the proper choice of first function and second function is significant Try integrating Taking x as the first function and e x as the second function is simpler than taking x as the second function. (2) Integrating by parts may not be..
(1) While integration by parts, the proper choice of first function and second function is significant Try integrating Taking x as the first function and e x as the second function is simpler than taking x as the second function. (2) Integrating by parts may not be..Method:
(ii) Find the values of the constants L and M by comparing the co-efficients of like powers of x on both sides. (iv) The integrals in the form are easily integrable..
(ii) Find the values of the constants L and M by comparing the co-efficients of like powers of x on both sides. (iv) The integrals in the form are easily integrable..Frictional Effects
/m, or the resistive force per unit mass per unit velocity, is often denoted by 2k, where k is called damping constant of the medium. where C is a constant of integration to be determined from the initial conditions. Thus, if at t = 0, v = v 0 , we have log e..
/m, or the resistive force per unit mass per unit velocity, is often denoted by 2k, where k is called damping constant of the medium. where C is a constant of integration to be determined from the initial conditions. Thus, if at t = 0, v = v 0 , we have log e..See what our Users say :
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