# Integration as the limit of a sum

Find the integral by the method of summation the values of :-

(a) integral of e^(-x) where the range of integration is from a to b.

(b) integral of e^(kx) where the range of integration is from a to b.

https://brainmass.com/math/integrals/integration-limit-sum-23619

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Integration as the limit of a sum

Written by :- Thokchom Sarojkumar Sinha

Find the integral by the method of summation the values of :-

b b

(a) âˆ« e-x dx (b) âˆ« ekx dx

a a

b n-1

Solution :- âˆ« e-x dx = Lt h âˆ‘ e-(a + rh) , where nh = b - a

a hâ†’0 r = 0

= Lt h [ e-a + e-(a+h) + e-(a+2h) + ........+ e-{a+(n-1)h}]

hâ†’0

...

#### Solution Summary

This solution is comprised of a detailed explanation for finding the integral by the method of summation the values.

It contains step-by-step explanation for finding the integral by the method of summation the values of :-

(a) integral of e^(-x) where the range of integration is from a to b.

(b) integral of e^(kx) where the range of integration is from a to b.

Solution contains detailed step-by-step explanation.