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

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

What could the dimensions of the floor be in terms of x, Harold is tiling a...

Harold is tiling a rectangular kitchen floor with an area that is expressed as x 2 + 6x + 5. What could the dimensions of the floor be in terms of x? Because area of a rectang

Fractions, #question.mario has 3 nickelsin his pocket.wha fraction ofadolla...

#question.mario has 3 nickelsin his pocket.wha fraction ofadolla do 3 nickels represent

Hierarchical multiple regression, A group of children who lived near a lead...

A group of children who lived near a lead smelter in El Paso, Texas, were identified and their blood levels of lead were measured. An exposed group of 46 children were identified w

Project, report on shares and dovidend using newspaper

report on shares and dovidend using newspaper

Fraction, how do you learn about equivelant fractions

how do you learn about equivelant fractions

Partial derivatives, So far we have considered differentiation of functions...

So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable

F distribution, The F Distribution The F distribution is the dis...

The F Distribution The F distribution is the distribution of the ratio of 2 random variables. Both random variables have yet another distribution, called the c 2 Distri

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