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

NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS, Our objective is solve the follo...

Our objective is solve the following fourth-order BVP: (a(x)u'' )'' = f (x) u(0) = u(1)=0 u(0)' = u(1)'=0 (a) Give the variational formulation of the above BVP. (b) Describe the

Chapter problem temperature around the globe.., predict whether there is a ...

predict whether there is a relationship between the mean January temperatures of a city in North America and the city''s position west of the prime meridian.

Quantitative Technique in Marketing, a company''s advertising expenditures ...

a company''s advertising expenditures average $5,000 per month. Current sales are $29,000 and the saturation sales level is estimated at $42,000. The sales-response constant is $2,

Sqrt n- sqrt 8836, How many integers satisfy (sqrt n- sqrt 8836)^2 Solutio...

How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence  93 8649  the number o

What is the cost to generate, The production costs per week for generating ...

The production costs per week for generating x widgets is given by, C ( x ) = 500 + 350 x - 0.09 x 2 ,         0 ≤ x ≤ 1000 Answer following questions.  (a) What is the c

Complementary addition model, E1) How is the 'comparison model' different...

E1) How is the 'comparison model' different from the 'complementary addition model'? E2) Create one word problem related to the children's world for each of the 4 models liste

Grouping-categories of situations requiring division , Grouping - situatio...

Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t

Matric, fgdg ggghfr hhrhfrf hfrrg jhj hjgg dear friend ghr tu vgu jyyiu ui ...

fgdg ggghfr hhrhfrf hfrrg jhj hjgg dear friend ghr tu vgu jyyiu ui u huik bgyuiiyts husk

Developing an understanding of subtraction, DEVELOPING AN UNDERSTANDING O...

DEVELOPING AN UNDERSTANDING OF SUBTRACTION :  The process of subtraction is the reverse of that of addition. Adding more to a collection to make it bigger is just the reverse

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