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

Write the value of sin10+sin20+sin30+....+sin360., sin10+sin20+sin30+....+s...

sin10+sin20+sin30+....+sin360=0 sin10+sin20+sin30+sin40+...sin180+sin(360-170)+......+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360 sin360-x=-sinx hence all terms cancel

What is a mixed number, Q. What is a Mixed Number? Ans. A mixed nu...

Q. What is a Mixed Number? Ans. A mixed number is an integer, along with a fractional part, which has the same sign. (Therefore, a mixed number always has two parts.) M

Holistic Marketing, Do you believe the holistic marketing concept is the mo...

Do you believe the holistic marketing concept is the most effective way to conduct marketing activities? Why? (Why not?)

Homomorphism, Let G be a group acting on a set X. The action is called fait...

Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov

Find the lesser of two consecutive positive even integers, Find the lesser ...

Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k

Determine all possible solutions to ivp, Determine all possible solutions t...

Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th

Evaluate the integral - trig substitutions, Example of Trig Substitutions ...

Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo

Geometry, #question.onstruct/draw geometric shapes with specific condition....

#question.onstruct/draw geometric shapes with specific condition.

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