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

Phase plane, Before proceeding along with in fact solving systems of differ...

Before proceeding along with in fact solving systems of differential equations there's one topic which we require to take a look at. It is a topic that's not at all times taught in

Determine the position and nature of stationary points, Question. Deter...

Question. Determine the position and nature of stationary points of the function? f(x,y)= y/x -x 2 +y 2

Canada australia eire spain, Before independence, Bangladesh was called Cey...

Before independence, Bangladesh was called Ceylon East Pakistan Bhutan Bangalore Which of the following countries does not have a monarch as head of state? Canada Australia Eire

Partial fractions - integration techniques, Partial Fractions - Integration...

Partial Fractions - Integration techniques In this part we are going to take a look at integrals of rational expressions of polynomials and again let's start this section out w

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

Algebra, sir/madam, i abdulla working as a maths teacher want to join ur es...

sir/madam, i abdulla working as a maths teacher want to join ur esteemed organisation as a tutor how can i proceed i have created an account even pls guide me, thanks abdulla

Divides a given line segment internally in the ratio of 1:3, Divides a give...

Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let

Phase transformations in binary system, Get the Delta H (Enthalpy) and Delt...

Get the Delta H (Enthalpy) and Delta V (Volume) of the both components below and compare by ratio.  You need to use clapeyron equation and also need to draw the graphs. S A LG

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