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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.
Integration by Parts -Integration Techniques Let's start off along with this section with a couple of integrals that we should previously be able to do to get us started. Fir
QUESTION (a) A bowl contains ten red balls and ten blue balls. A woman selects balls at random without looking at them. i) How many balls must she select to be sure of havin
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Fermat's Theorem : If f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f
A sinking ship signals to the shore for assistance. Three individuals spot the signal from shore. The ?rst individual is directly perpendicular to the sinking ship and 20 meters in
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Suppose S = {vi} and T = {ti} are "easy" sets of knapsak weight. Also, P and q are primes p > ?Si and q > ?ti. We can combine S and T into a signle set of knapsack weight as follow
If y 1 (t) and y 2 (t) are two solutions to a linear, homogeneous differential equation thus it is y (t ) = c 1 y 1 (t ) + c 2 y 2 (t ) ........................(3) Remem
HOW TO ADD MIXED FRACTION
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