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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.
Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures
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What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems
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OPERATION RESEARCH ABSTRACT
Let's take a look at one more example to ensure that we've got all the ideas about limits down that we've looked at in the last couple of sections. Example: Given the below gr
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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
The remainder when 5^99 is divided by 13 Ans) 8 is the remainder.
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