Question

iviaincu vului 1.UU
In order to express infinite series as definite
integral,
A. sign of summation is replaced by integration.
B. sign of integration is replaced by summation.
C. infinite series can't be expressed as definite
integral.
D. None of the above​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

In order to express infinite series as definite. integral

A. sign of summation is replaced by integration.

B. sign of integration is replaced by summation.

C. infinite series can't be expressed as definite

integral.

D. None of the above

EVALUATION

Integration

The actual proces of finding the function, when its derivative or its differentiation is is known, is called integration as anti-derivative. The function to which the integration is applied is called Integrand and the function obtained as a result is said to be Integral.

The Definite Integral will be regarded as a sum or more correctly the limit of a sum of simple elements as their number becomes greater and greater without bound and at the same time as each element becomes infinitesimally small

The Definite Integral is written as

$\displaystyle \sf{ \int\limits_{a}^{b} \: f(x) \, dx }$

The above Definite Integral geometrically represents the area of the region enclosed by the curve y = f(x), the x axis and the ordinates at x = a and x = b

With usual notation a is called lower limit , b is called upper limit

In terms of limit of a sum

$\displaystyle \sf{ \int\limits_{a}^{b} \: f(x) \, dx } = \displaystyle \sf{\lim_{n \to \infty } \: \frac{b - a}{n} \: \: \displaystyle \sf{ \sum\limits_{r=0}^{n - 1} \: f \bigg(a + \frac{b - a}{n} \: . \: r \bigg)}}$

Hence from above we can conclude that

In order to express infinite series as definite

integral sign of summation is replaced by integration

FINAL ANSWER

Hence the correct option is

A. Sign of summation is replaced by integration

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Answer 2

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• Option A is correct.