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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.
Q. Illustrate Field Properties of Numbers? Ans. What the associative law of addition states is this: for any numbers a, b, and c,
The students of a class are made to stand in complete rows. If one student is more in each row, there would be 2 rows less, and if one student is less in every row, there would be
Non Zero Sum Games Recently there was no satisfactory theory either to describe how people should play non-zero games or to explain how they actually play that game Nigel Ho
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1) At a midway game at the state fair, the probability of winning an individual game is advertised to be 30% ( p = . 3). Suppose 50 people played the game (assume all 50 outcomes
A pair of pants costs $24. The cost was decreased by 8%. What is the new cost of the pants? If the cost of the pants is decreased by 8%, the cost of the pants is 92 percent of
What is the greater of two consecutive negative integers whose product is 132? Let x = the lesser integer and let x + 1 = the greater integer. Because product is a key word for
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Theorem Consider the subsequent IVP. y′ = p (t ) y = g (t ) y (t 0 )= y 0 If p(t) and g(t) are continuous functions upon an open interval a o , after that there i
Product Moment Coefficient (r) This gives an indication of the strength of the linear relationship among two variables. N
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