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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.
Changing The Base Of The Index For comparison reasons if two series have different base years, this is difficult to compare them directly. In such cases, it is essential to ch
How to solve this: log x(81) = 4
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Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x) dx Solution This kind of integral approximately falls into the form given in 3c. It is a quotient of ta
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You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in two weeks. You decide to hire a moving company, but are
Determine a particular solution for the subsequent differential equation. y′′ - 4 y′ -12 y = 3e5t + sin(2t) + te4t Solution This example is the purpose that we've been u
GUESS THE NUMBER THAT WHEN YOU SUBTRACT 6 AND THEN SUBTRACT 0 IS-14
In the earlier section we modeled a population depends on the assumption that the growth rate would be a constant. Though, in reality it doesn't make much sense. Obviously a popula
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