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

Subtraction of like terms with same signs, Suppose we are required to...

Suppose we are required to find the difference between 3abc and 7abc. We look at two scenarios. The value we would obtain by subtracting a larger quantity from th

Question, Hi I have a maths question related to construction as its a cons...

Hi I have a maths question related to construction as its a construction management course...i could send some example sheets too...could it be done?

How long will he have to ride to burn 750 calories, Jeff burns 500 calories...

Jeff burns 500 calories per hour bicycling. How long will he have to ride to burn 750 calories? To find out the number of hours required to burn 750 calories, divide 750 throug

Standard deviation, Certain model of new home distributed with a mean of $1...

Certain model of new home distributed with a mean of $150,000. Find percentage of buyers who paid between $150,000-155,000 if standard deviation is $1800.

ConnectEd, How do I increase and decrease tax and sales

How do I increase and decrease tax and sales

Tests for relative minimum, Tests for relative minimum For a relative ...

Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx)  = f´(x) = 0 ii.The second derivative, which i

Ecercises, ne nje tabak letre me permasa 100cm dhe 55cm nje nxenes duhet te...

ne nje tabak letre me permasa 100cm dhe 55cm nje nxenes duhet te ndertoje nje kuboide me permasa 20cm,25cm,40cm. a mund ta realizoje kete, ne qofte se per prerjet dhe ngjitjet humb

Recognizes the absolute extrema & relative extrema, Recognizes the absolute...

Recognizes the absolute extrema & relative extrema for the following function.                           f ( x ) = x 2       on [-1, 2] Solution:  As this function is simpl

Polynomials, for what value of k,the following system of equations have inf...

for what value of k,the following system of equations have infinite solutions?kx + 5y -(k-5)=0;20x +ky - k=0

Find the maxima or minima and green theorem, 1) find the maxima and minima ...

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

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