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

What was brian''s total commission on these three sales, Brian is a real es...

Brian is a real estate agent. He forms a 2.5% commission on each sale. During the month of June he sold three houses. The houses sold for $153,000, $299,000, and $121,000. What was

Probability, You''ve decided you want a plant for your room. At the gardeni...

You''ve decided you want a plant for your room. At the gardening store, there are 444 different kinds of plants (tulip, fern, cactus, and ficus) and 444 different kinds of pots to

Original price of the mittens was $10 what is the new price, A pair of mitt...

A pair of mittens has been discounted 12.5%. The original price of the mittens was $10. What is the new price? Find 12.5% of $10 and subtract it from $10. Find out 12.5% of $10

What was the total cost of her order, Leslie ordered a slice of pizza for $...

Leslie ordered a slice of pizza for $1.95, a salad for $2.25, and a soda for $1.05. What was the total cost of her order? The cost of every item must be added together; $1.95 +

Intermediate value theorem, Intermediate Value Theorem Suppose that f(x...

Intermediate Value Theorem Suppose that f(x) is continuous on [a, b] and allow M be any number among f(a) and f(b).   There then exists a number c such that, 1. a 2. f (

Geometry, How do you solve (17+w)^2 + w^2 = (25+w)^2

How do you solve (17+w)^2 + w^2 = (25+w)^2

Equations, At a bakery the cost of 30 experts is 45$. Write an equation tha...

At a bakery the cost of 30 experts is 45$. Write an equation that shows the cost of 45 cookies

Multiplicative rule - rules of probability, Multiplicative Rule - Rules of ...

Multiplicative Rule - Rules of Probability It is used when there is a string of independent events for that individual probability is known and it is essential to know the ove

Geometria, un prisma retto ha per base un rombo avente una diagonale lunga ...

un prisma retto ha per base un rombo avente una diagonale lunga 24cm. sapendo che la superficie laterale e quella totale misurano rispettivamente 2800cm e3568cm ,calcola la misura

How many permutations can you make of the word statistics, Q. How many perm...

Q. How many permutations can you make of the word STATISTICS? Solution:  There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'

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