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

Determine the transfer function, A digital filter has zero at z=a and poles...

A digital filter has zero at z=a and poles at z=b andz=c, where a, b, c are the real constants. Determine the transfer function and the frequency response function of the filter an

Definition and fact of the shape of a graph, Definition 1.   Given any ...

Definition 1.   Given any x 1  & x 2   from an interval  I with x 1 2  if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2.   Given any x 1  & x 2  from an interval

Calculate the cost make use of trigonometric functions, In this task you ar...

In this task you are required to make use of trigonometric functions, research and use the Monte Carlo method of integration to determine areas under curves and perform calculation

Minimizes the sum of the two distance, The value of y that minimizes the su...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

Explain different base numbers, Explain Different Base Numbers? In mult...

Explain Different Base Numbers? In multiplying or dividing two exponential expressions with different base numbers, write out the exponential expressions as products. Since

Time & distance., Q4. Assume that the distance that a car runs on one liter...

Q4. Assume that the distance that a car runs on one liter of petrol varies inversely as the square of the speed at which it is driven. It gives a run of 25km per liter at a speed o

What is exponents values, What is Exponents values? Exponents were inve...

What is Exponents values? Exponents were invented as a quick way to show that you are multiplying a number by itself several times. It's too much trouble to write something

Angles, samuel left mauritius at 22:30 on saturday and travelled to london ...

samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min

An even function, Assume that   i)  Determine all the roots of f...

Assume that   i)  Determine all the roots of f(x) = 0. ii)  Determine the value of k that makes h continuous at x = 3. iii)  Using the value of k found in (ii), sh

What percent of her money did she spend on lunch, Wendy brought $16 to the ...

Wendy brought $16 to the mall. She spent $6 on lunch. What percent of her money did she spend on lunch? Divide $6 by $16 to ?nd out the percent; $6 ÷ $16 = 0.375; 0.375 is equi

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