Example of infinite interval - improper integrals, Mathematics

Assignment Help:

Evaluate the subsequent integral.

1088_Example of Infinite Interval - Improper Integrals 1.png

Solution

This is an innocent enough looking integral. Though, because infinity is not a real number we cannot just integrate as normal and after that "plug in" the infinity to get the answer, to see how we are going to do this type of integral let's think of this like an area problem. Thus in place of asking what the integral is, let's in place of ask what the area within f (x) = 1/x2 on the interval [1, ∞] is. Till we are not able to do this, though, let's step back a little and instead ask what the area within f (x) is on the interval [1, t] where 1 > t and t is finite. This is a difficulty that we can do.

21_Example of Infinite Interval - Improper Integrals 2.png

Now, we can get the area under f(x) on [1, ∞] simply by taking the limit of at like t goes to infinity.

1513_Example of Infinite Interval - Improper Integrals 3.png

After that this is how we will do the integral itself.

1276_Example of Infinite Interval - Improper Integrals 4.png


Related Discussions:- Example of infinite interval - improper integrals

Estimation of difference among two means-illustration, A comparison of the ...

A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and

..Job, Eddie mkes $15.75 per hour. Estimate how much Eddie will make per ye...

Eddie mkes $15.75 per hour. Estimate how much Eddie will make per year if he works 40 hours per week and 50 weeks per year.

Difference between experiment and outcome, Difference Between Experiment an...

Difference Between Experiment and Outcome Experiment is an operation that produces outcomes which can be observed. Outcome/Event is the result of an experiment.

Definition of relation, Definition of Relation A relation is a set of o...

Definition of Relation A relation is a set of ordered pairs. It seems like an odd definition however we'll require it for the definition of a function though, before actuall

How much is invested at 8% if the total amount of interest, Kevin invested ...

Kevin invested $4,000 in an account which earns 6% interest per year and $x in a different account that earns 8% interest per year. How much is invested at 8% if the total amount o

Help, How do I solve step by step 7

How do I solve step by step 7

Circls, in a given figure a,b,c and d are points on a circle such that ABC ...

in a given figure a,b,c and d are points on a circle such that ABC =40 and DAB= 60 find the measure of DBA

Sum, i want to trick to know how can i fastest calculate more than compute...

i want to trick to know how can i fastest calculate more than computer

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd