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

Linear programming, As office manager of her firm, Marcellyne has been dir...

As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic

Simple interest, write a program C++ programming language to calculate sim...

write a program C++ programming language to calculate simple interest, with it algorithm and it flowchart

What kinds classroom activities help children to learn maths, What kinds of...

What kinds of classroom activities can you think of for helping children to make groups of 5 and 10? Once they have enough practice with such activities, children can be helped

Straight Line, can i known the all equations under this lesson with explana...

can i known the all equations under this lesson with explanations n examples. please..

Relationship between the graph and inverse function, Interesting relationsh...

Interesting relationship between the graph of a function and the graph of its inverse : There is one last topic that we have to address quickly before we leave this section.  Ther

Graph f(x) = ex and g(x) = e- x - common graph, Graph f ( x ) = e x and g ...

Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.

Triangle Treat, Triangle Treat is the page name. I don''t know the answer f...

Triangle Treat is the page name. I don''t know the answer for it, can someone give it to me?

Core concepts of marketing, examination questions and answers to the above ...

examination questions and answers to the above title.

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