Register to reply

Integrals of vector functions

by autodidude
Tags: functions, integrals, vector
Share this thread:
Nov29-12, 03:22 PM
P: 333
What is the geometrical significance of the definite integral of a vector function if any?

e.g. if you integrate a vector function that gives the velocity of some particle between t1 and t2, the vector we get indicates the distance travelled in the i, j and k directions right? does the direction of this vector have any meaning? Also, is there a geometric interpretation of this value like area under the curve for the definite integral of a scalar function?
Phys.Org News Partner Mathematics news on
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
Nov29-12, 03:57 PM
P: 1,212
specifically the integral of the velocity vector over time will give you the displacement vector, and the direction of this points in the direction of the particle's position at t2 relative to its position at t1.

I'm not sure what you want for a geometric interpretation. There are three curves and three areas- the distances travelled in each of the three directions of i, j and k.
Nov29-12, 05:31 PM
P: 333
Thanks. nah i was just wondering if there was somehow an area interpretation like with scalar functions

Register to reply

Related Discussions
Spherical Vector Wave Functions and Surface Green's Functions Advanced Physics Homework 0
Integrals with bessel functions General Math 3
Integrals and Inverse Functions Calculus & Beyond Homework 4
Orthogonal functions and integrals. Calculus 0
Integrals of vector functions Introductory Physics Homework 2