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

Convert the points into cartesian and polar coordinates, Convert each of th...

Convert each of the following points into the specified coordinate system.  (a) (-4, 2 Π /3) into Cartesian coordinates. (b) (-1,-1) into polar coordinates.  Solution

Organized list strategy, i can not figer out my homework it says "USE THE M...

i can not figer out my homework it says "USE THE MAKE AN ORGANIZED LIST STRATEGY,Medeline bikes 4 laps around her neighborhood 2 times a week.How many laps does she bike in 8 weeks

Formula to computing how much lumber to buy, Audrey is creating a increased...

Audrey is creating a increased flowerbed which is 4.5 ft by 4.5 ft. She requires computing how much lumber to buy. If she requires knowing the distance around the flowerbed, which

Partial Differential Equation, Determine the minimum capacity C of a Capaci...

Determine the minimum capacity C of a Capacitor given that: C =(ax/(x-a))+(xy/(y-b))+(yb/(b-y)) given that "a" and "b" are fixed values and "x" and "y" vary independently such th

Objectives to knowing your maths learner, Objectives After studying th...

Objectives After studying this unit, you should be able to briefly describe the developmental stages of children's thinking and learning processes; assess the levels

Shoppers` stop, 3. How are Indian customers visiting Shoppers’ Stop any dif...

3. How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries? 4. How should Shoppers’ Stop develop its demand forecasts?

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