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

Intergration, Functional and variations.Block III, Consider the functiona...

Functional and variations.Block III, Consider the functional S[y]=?_1^2 v(x^2+y'')dx , y(1)=0,y(2)=B Show that if ?=S[y+eg]-S[y], then to second order in e, ?=1/2 e?_1^2¦?g^'

One of these food groups, In a collection of 30 dissimilar birds, 15 eat wo...

In a collection of 30 dissimilar birds, 15 eat worms, 18 eat fruit, and 12 eat seeds. Accurately 8 eat worms and seeds, 8 eat worms and fruit, 7 eat fruit and seeds, and 4 eat each

Fact of the wronskian method, Given two functions f(x) and g(x) which are d...

Given two functions f(x) and g(x) which are differentiable on some interval I  (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int

Analysis and optimization, 1. In an in finite horizon capital/consumption m...

1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production

Calculate values of the derivative, First, see that the right hand side of ...

First, see that the right hand side of equation (2) is a polynomial and thus continuous. This implies that this can only change sign if this firstly goes by zero. Therefore, if the

Ratios, in a veggie mix the ratio of cups of carrots to cups of broccolie i...

in a veggie mix the ratio of cups of carrots to cups of broccolie is 4 to 5 if you made this party mix larger how many cups of carrots would be needed to mix with fo cups of brocco

Examples of repetition need not be boring- learning maths, E1) Try and see ...

E1) Try and see the order in which different children fills numbers in the grid above. My claim is that all of them would fill in the ones, the fives and the tens first. Test my hy

Estimate the loss to the bank - restructure the loan, Your bank has a loan ...

Your bank has a loan outstanding with a current balance of $1,000,000 that is payable in quarterly equal instalments of $49,924.  This loan has another 6 years to maturity.  The bo

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