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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
Example of Subtraction of Fractions: 1/3 + 1/6 + 1/8 = ____ Using trial & error we could search that 24 is the LCD or smallest number in which 3, 6, and 8 will all divide w
The conjugate of the complex number a + b i is the complex number a - b i . In other terms, it is the original complex number along the sign on the imaginary part changed. Here
design a synchronous, recycling, MOD-12 counter with D FF''s. Use the states 0000 through 1011 in the counter.
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x=+y^2=4
I need an explanation of "the integral, from b to a, of the derivative of f (x). and, the integral from a to b. of the derivative of f(t) dt.
If a telephone pole weighs 11.5 pounds per foot, how much does a 32-foot pole weigh? Multiply 11.5 by 32; 11.5 × 32 = 368 pounds.
Calculate the introduction to Probability? Probability refers to the chance that an event will happen. Probability is presented as the ratio of the number of ways an event can
Explain Linear Equations ? Set of ordered pairs of numbers A set is an undefined term and we describe it as a "well defined" collection. We use the symbol "{ }" to denote "a se
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
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