Integration variable, Mathematics

Assignment Help:

Integration variable : The next topic which we have to discuss here is the integration variable utilized in the integral. In fact there isn't actually a lot to discuss here other than to note as well that the integration variable doesn't actually matter.  For instance,

∫x4 + 3x - 9 dx = (1/5) x5 + 3/2 x2 - 9x + c

∫t 4 +3t - 9 dt = 1 t 5 + 3 t 2 - 9t + c

∫w4 + 3w - 9 dw = 1 w5 + 3 w2 - 9w + c

Changing the integration variable in the integral merely changes the variable in the answer. It is significant to notice though that while we change the integration variable in the integral we also changed the differential (dx, dt, or dw) to match the new variable. it is more significant that we might realize at this point.

Another utilization of the differential at the ending of integral is to tell us what variable we are integrating with respect to. At this stage which may seem insignificant since mostly integrals which we're going to be working with here will only include a single variable.  Though, if you are on a degree track which will take you into multi-variable calculus it will be very significant at that stage as there will be more than one variable in the problem.  You have to get into the habit of writing the accurate differential at the end of the integral so while it becomes significant in those classes already you will be in the habit of writing it down.

To see why it is important take a look at the following two integrals.

∫ 2x dx                                              ∫ 2t dx

The first integral is simple enough.

                 ∫ 2x dx = x2 + c

The second integral is also rather simple, but we have to be careful. The dx tells us that we are integrating x's. That means that we integrate x's only which are in the integrand and all other variables in the integrand are assumed to be constants. Then the second integral is,

                                                    ∫ 2t dx = 2tx + c

Thus, it may appear silly to always put in the dx, however it is a vital bit of notation which can cause us to acquire the incorrect answer if we neglect to put it in.


Related Discussions:- Integration variable

Algebra, let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of...

let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?

Applications of de moiver, what are the applications of de moiver''s theore...

what are the applications of de moiver''s theorem in programming and software engineering

Compute the regular expression, 1. Consider the following context free gram...

1. Consider the following context free grammar G with start symbol S (we write E for the empty string, epsilon): S ---> bB | aSS A ---> aB | bAA B ---> E | bA | aS a. D

Conscious consumer, a group of 3o students is planning a thanksgiving party...

a group of 3o students is planning a thanksgiving party items needed hats @ $2.50 each.noise makers@$4.00 per pack of 5.Ballons @$5.00 per pack of 10.how many packs of noisemakers

Linear programming, As office manager of her firm, Marcellyne has been dir...

As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic

Can u please tell me how to solve, a triangle with side lengths in the rati...

a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3.what is the area of the triangle.

If a sequence is bounded and monotonic then it is convergent, Theorem ...

Theorem If {a n } is bounded and monotonic then { a n } is convergent.  Be cautious to not misuse this theorem.  It does not state that if a sequence is not bounded and/or

Inverse tangent, Inverse Tangent : Following is the definition of the inve...

Inverse Tangent : Following is the definition of the inverse tangent.  y = tan -1 x     ⇔ tan y = x                     for            -∏/2 ≤ y ≤ ?/2 Again, we have a limi

Fractions, my daughter brought home home work im not sure how to do it the ...

my daughter brought home home work im not sure how to do it the fractions has to be labled from least to greatest

Probability, I don''t understand the AND/OR rules and how they apply to pro...

I don''t understand the AND/OR rules and how they apply to probability

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