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

Average cost function, Average cost function : Now let's turn our attentio...

Average cost function : Now let's turn our attention to the average cost function. If C ( x ) is the cost function for some of the  item then the average cost function is,

Multiplication and division , In multiplication and division we have 1) ...

In multiplication and division we have 1) Suggested ways of conveying the meaning of multiplication and division to children. These operations have to be taught as an activit

Maths, what is the diameter of a circle

what is the diameter of a circle

Trade discount, on 30 april, anthony purchased television invoiced at rm 69...

on 30 april, anthony purchased television invoiced at rm 6999 with cash discount terms of 2/10, 1/15, n/30 and also a trade discount 1.5%, 2%, 3.25%. In order to pay the invoice, h

Truth criteria-nature of mathematics, Truth Criteria :  Consider the follo...

Truth Criteria :  Consider the following statements: i) Peahens (i.e., female peacocks) lay eggs around September. ii) Water boils at 100°C. iii) 5 divides 15 without lea

Fraction word problems, Alan had 6 books. He read 1/3 of books last week. ...

Alan had 6 books. He read 1/3 of books last week. How many books did Alan read last week?

Solid mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Alcohol solution (mixture), Nora works at a laboratory as a chemist . she w...

Nora works at a laboratory as a chemist . she was told to prepare 100L of 25% alcohol solution. she has on hand of a 15% percent alcohol solution and a 40% alcohol solution which s

Linear Programming, describe phases of operations research study ?

describe phases of operations research study ?

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