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) ∫ e-x dx (b) ∫ ekx dx
a a
b n-1
Solution :- ∫ e-x dx = Lt h ∑ e-(a + rh) , where nh = b - a
a h→0 r = 0
= Lt h [ e-a + e-(a+h) + e-(a+2h) + ........+ e-{a+(n-1)h}]
h→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.