Smooth curve - three dimensional space, Mathematics

Assignment Help:

Smooth Curve - Three Dimensional Space

A smooth curve is a curve for which r' (t) is continuous and r' (t) ≠ 0 for any t except probably at the endpoints. A helix is a smooth curve, for instance.

At last, there is requirement of discuss integrals of vector functions. By using both limits and derivatives like a guide it shouldn't be too surprising that we as well comprise the following for integration for indefinite integrals

∫ r (t) = {∫ f (t)dt, ∫g (t)dt, ∫ h(t) dt} + c

∫ r (t) = ∫ f (t)dt i+ ∫g (t)dt j+ ∫ h(t) dt} k  + c

and the following for definite integrals.

ba r (t) dt = {∫ba f (t) dt, ∫ba g (t) dt, ∫ba h(t) dt}

ba r (t) dt = ∫ba f (t) dt i + ∫ba g (t) dt j + ∫ba h(t) dt k

Along with the indefinite integrals we put in a constant of integration to ensure that it was clear that the constant in this case requires being a vector in place of a regular constant.


Related Discussions:- Smooth curve - three dimensional space

Sketch the graph of the derivative of this function f '( x), Below is the s...

Below is the sketch of a function f ( x ) . Sketch the graph of the derivative of this function f ′ ( x ) . Solution : At first glance it seems to an all however impossib

Least cost method in operations research, algorithm and numerical examples ...

algorithm and numerical examples of least cost method

Video games, Should video game companies continue to alter their products t...

Should video game companies continue to alter their products to include other functions, such as e-mail

Tables and funcuctions, write an equation for a functionthat gives the valu...

write an equation for a functionthat gives the value in ech table .

Compound and simple interest, Your grandparents gave you a gift of R2 000 o...

Your grandparents gave you a gift of R2 000 on your 16th birth day. You want to invest the money in an account over four years. You have an option of investing the R2 000 at 8% per

#title.simpal harmonic motion., #questionShow that the system oscillates in...

#questionShow that the system oscillates in simple harmonic motion demonstrated by; , for which the general solution where X = (x – x0)..

Mathematical concepts and ideas , These experiences should be related to th...

These experiences should be related to the mathematical concepts and ideas that we teach them. Only then will these ideas appear relevant to the children, and be absorbed by them

Example to compute limit, calculates the value of the following limit. ...

calculates the value of the following limit. Solution Now, notice that if we plug in θ =0 which we will get division by zero & so the function doesn't present at this

Determine the area of the book jacket, A publishing company is creating a b...

A publishing company is creating a book jacket for a newly published textbook. Determine the area of the book jacket, given that the front cover is 8 in wide by 11 in high, the bin

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