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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.
Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these
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Graph y = sin ( x ) Solution : As along the first problem in this section there actually isn't a lot to do other than graph it. Following is the graph. From this grap
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The form x2 - bx + c ? This tutorial will help you factor quadratics that look something like this: x 2 -7x + 12 (No leading coefficient; negative middle coefficient; p
(x*1)+(x*7) =
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Describe Three Ways to Write Negative Fractions? There are three different ways that a negative fraction can be written. They are all represent the same value. 1. The negative
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what''s the main purpose of algebra in our daily life
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