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

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

integration: if f(x)+f(x+1/2) =1 find limit 0 to 2, f(x)+f(x+1/2) =1 f(x...

f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1

The alternative hypothesis, The alternative hypothesis When formulatin...

The alternative hypothesis When formulating a null hypothesis we also consider the fact that the belief may be found to be untrue thus we will refuse it.  Therefore we formula

Solution of triangles, In triangle ABC, if sinA/csinB+sinB/c+sinC/b=c/ab+b...

In triangle ABC, if sinA/csinB+sinB/c+sinC/b=c/ab+b/ac+a/bc then find the value of angle A.

Need some clarity?, THE % PARTICIPATION Feature in a major medical expense ...

THE % PARTICIPATION Feature in a major medical expense policy is 75% with a $100 deductible. how much of a $2,000 bill is the insured responsible for paying?

The equation of the tangent, Consider the function f(x) = 2x 2 + 1. Find ...

Consider the function f(x) = 2x 2 + 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use first principles.

Quadratic Functions, Can you please explain what Quadratic functions are?

Can you please explain what Quadratic functions are?

Density Determination, If the mass is 152.2g and the volume is 18cm3, then ...

If the mass is 152.2g and the volume is 18cm3, then what is the density?

Factor Fiction, Ok this is true or false wit a definition. The GCF of a pai...

Ok this is true or false wit a definition. The GCF of a pair of numbers can never be equal to one of the numbers.

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