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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 following interpolation problem: Find a quadratic polynomial p(x) such that p(x0) = y0 p’(x1) = y’1 , p(x2) = y2 where x0 is different from x2 and y0, y’1 , y2 a
What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32
-8 plus (-17)
1 Data is to be transmitted over Public Switched Telephone Network (PSTN) using 8 levels per signaling elements. If the bandwidth is 3000 Hz, deduce the theoretical maximum transfe
define algorithm of pert and pert with suitable examples
r=asin3x
In this theorem we identify that for a specified differential equation a set of fundamental solutions will exist. Consider the differential equation y′′ + p (t ) y′ + q (t
1. A drainage system overflows into a river causing pollution when the rainfall falling in an hour exceeds 50 mm. During any given year, the maximum hourly rainfall follows an expo
To solve out linear equations we will make heavy use of the following facts. 1. If a = b then a + c = b + c for any c. All it is saying that we can add number, c, to both sides
a product can be anything including physical good,services,places,experience,nations,organizations,properties,information.discuss the statement?
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