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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.
1x1
A pipe has a diameter of 2.5 inches. Insulation which is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe along with the insulation around it? The i
Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we
47x+33y=143
A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =
Definition 1. Given any x 1 & x 2 from an interval I with x 1 2 if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2. Given any x 1 & x 2 from an interval
1.What are the strengths and shortcomings of the methods of teaching H T 0 in Examples 1 and 2? 2. a) Think of another activity for getting children to practise H T 0, especia
INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the
sequencing problem
It is the catch all force. If there are some other forces which we decide we need to act on our object we lump them in now and call this good. We classically call F(t) the forcing
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