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Difference between summation and integration

What is the difference between summation and integration?

  • Himanshu
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5 उत्तर

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  • Summation involves the discrete values with the upper and lower bounds, whereas the integration involves continuous value.Summation is a process of discrete addition while Integration is a process of adding continuous things.

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  • The use of emSummation/em arises when there is need of discrete sum of quantities( i.e. addition of few distinct numbers or even large series);br /emIntegration/em is used when the addition is not limited to few or more discrete quantities embut /emthe addition is to be done on a continuous basis.br /In short, strongSummation/strong= Discrete addition strong:Integration= /strongContinuous addition.br /br /This area can be given as the sum of much smaller areas included in the bounded area. But Summation involves the discrete values with the upper and lower bounds, whereas the integration involves continuous value.br /Summation is a process of discrete addition while Integration is a process of adding continuous things.

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  • strongSummation/strong, as the name suggests is used when we have to add up the numbers.br /Represented as ∑br /strongIt is used when we have a discrete set of numbers/strongbr /br /strongIntegration/strong is used to find the area, volume of a given functionbr /Represented asbr /∫ a b f ( x ) d xbr /strongIt is used when we have a continuous set of numbers/strongbr / 

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  • Summation is adding up of a sequence of numbers. Usually, the summation is given in this form ∑ni=1 aiwhen the terms in the sequence have a pattern and can be expressed using a general term.br /br / Integration is basically the area bounded by the curve of the function, the axis and upper and lower limits. This area can be given as the sum of much smaller areas included in the bounded area.

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