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

Direction fields, This topic is specified its own section for a couple of p...

This topic is specified its own section for a couple of purposes. Firstly, understanding direction fields and what they tell us regarding a differential equation as well as its sol

How many dollars did they raise the first two days, The freshman class is p...

The freshman class is participating in a fundraiser. Their target is to raise $5,000. After the first two days of the fundraiser, they have raised 32 percent of their goal. How man

Tent originally sold for $2 what is the percent of discount, A tent origina...

A tent originally sold for $260 and has been marked down to $208. What is the percent of discount? Find out the number of dollars off. $260 - $208 = $52. Further, determine wha

About algebra, how do i compute an algebra number

how do i compute an algebra number

Probability, TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 N...

TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 NOON.  THE FIRST ONE TOARRIVE WAITS FOR 20 MIN AND THEN LEAVE. IF THE TIME OF THIR ARRIVAL BE INDEPENDET AND AT RNDOM,T

probability , An engineer has 200 resistors that he keeps in one box. Resi...

An engineer has 200 resistors that he keeps in one box. Resistors are colored to help their identification, and in this box there are 30 white resistors, 50 black resistors, 80 red

Rectilinear figures, Q1- different types of rectilinear figures? Q2- interi...

Q1- different types of rectilinear figures? Q2- interior and exterior angles of the polygon? Q3-relation between interior and exterior angles of polygons? Q4- properties of any fiv

Determine the fraction of the time, Ipswich has two ambulances. Ambulance 1...

Ipswich has two ambulances. Ambulance 1 is based at the local college and ambulance 2 is based downtown. If a request for an ambulance comes from the local college, the college-bas

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