Purchase Solution

# Integration as the limit of a sum

Not what you're looking for?

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.

##### 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.

##### Solution Preview

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 provided by:
###### Education
• BSc, Manipur University
• MSc, Kanpur University
###### Recent Feedback
• "Thanks this really helped."
• "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
• "Very nice thank you"
• "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
• "You are awesome. Thank you"

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.