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

Determine and classify all critical points , Determine and classify all the...

Determine and classify all the critical points of the given function.  Described the intervals where function is increasing & decreasing. Solution: Firstly we'll require

Describe square roots, Describe Square Roots? When a number is written ...

Describe Square Roots? When a number is written inside a radical sign (√), the number is called the radicand, and we say that you are "taking the square root of" that number.

The mean value theorem for integrals of even and odd , The Mean Value Theor...

The Mean Value Theorem for Integrals If  f (x ) is a continuous function on [a,b] then there is a number c in [a,b] such as,                                    ∫ b a f ( x

Algebra, find the value of A and B if the following polynomials are perfect...

find the value of A and B if the following polynomials are perfect square:

Congruences, Suppose m be a positive integer, then the two integer a and b ...

Suppose m be a positive integer, then the two integer a and b called congurent modulo m ' if a - b is divisible by m i.e.  a - b = m where is an positive integer. The congru

What was the total cost of the copies, Mary made 34 copies at the local off...

Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0

speed of the truck , A man travels 600km partly by train and partly by tru...

A man travels 600km partly by train and partly by truck. If he  covers 120km by train and the rest by truck, it takes him eight hours. But, if he travels 200km by train and the res

Solve sin (3t ) = 2 trig function, Solve sin (3t ) = 2 . Solution T...

Solve sin (3t ) = 2 . Solution This example is designed to remind you of certain properties about sine and cosine.  Recall that -1 ≤ sin (θ ) ≤ 1 and -1 ≤ cos(θ ) ≤ 1 .  Th

Evaluate the integral, Example:   If c ≠ 0 , evaluate the subsequent integr...

Example:   If c ≠ 0 , evaluate the subsequent integral. Solution Remember that you require converting improper integrals to limits as given, Here, do the integ

Mensuration, In an equilateral triangle 3 coins of radius 1cm each are kept...

In an equilateral triangle 3 coins of radius 1cm each are kept along such that they touch each other and also the side of the triangle. Determine the side and area of the triangle.

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