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

Inductive reasoning.., 2, -8, 32, -128, ?, ?, ?, what are these next 3?

2, -8, 32, -128, ?, ?, ?, what are these next 3?

1, use 3/8 of a thin of paint, what fraction of the paint is left in thin (...

use 3/8 of a thin of paint, what fraction of the paint is left in thin (show work

Eigenvalues and eigenvectors, If you find nothing out of this rapid review ...

If you find nothing out of this rapid review of linear algebra you should get this section.  Without this section you will not be capable to do any of the differential equations wo

Even and odd functions, Even and Odd Functions : This is the final topic ...

Even and Odd Functions : This is the final topic that we have to discuss in this chapter.  Firstly, an even function is any function which satisfies,

Algebra 1, how do you factor a trinomial into a binomial ?

how do you factor a trinomial into a binomial ?

Introduction to why learn mathematics, INTRODUCTION : All of us have encou...

INTRODUCTION : All of us have encountered mathematics while growing up. Some of us have grown to like it, and therefore, enjoy. doing it. Some others have developed a lukewarm rel

Trigonometry, how to work out consumer arithmetic?

how to work out consumer arithmetic?

The low temperature in Achorage, The low temperature in Anchorage, Alaska t...

The low temperature in Anchorage, Alaska today was negative four degrees. The low temperature in Los Angeles, California was sixty-three degreees. What is the difference in the two

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