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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.
Consider the function f(x) =1/2 (2 x +2 -x ) which has the graph (a) Explain why f has no inverse function. You should include an example to support your explanation
There may be more than one independent variable which determines the value of y. The dimension of a function is determined by the number of independent variables in the
When three quantities are in A.P., then the middle one is said to be the arithmetic mean of the other two. That is, if a, b and c are in A.P., then b is th
Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution: S = {(H, H), (H, T), (T, H
Find out all intervals where the given function is increasing or decreasing. f ( x ) = - x 5 + 5/2 x 4 + 40/3 x 3 + 5 Solution To find out if the function is increasi
Explain Simplifying Rational Expressions ? A rational expression, or algebraic fraction, is an expression in which you have a polynomial divided by a polynomial. Sometimes it
distance between pair of straight lines
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is that formula of sample and population for mean deviation is the same?
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