line integral of a curve (KristaKingMath)

In this video we'll learn how to find the line integral of a curve, when we're looking for the line integral under a function and over a line segment from one coordinate point to another coordinate point.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[zae]

Your video just saved one of Ph.D candidates in far east. Thank you.

[mumijuliya]

To be more specific these are parametric equations: x = 0+(1-0)t; y= 0+(2-0)t; z = 0+(3-0)t

[TheDaaani]

You are by far one of the best instructors of calculus online! Such clear explanations of the concepts and clear explanations of the calculations. Thank you so much!

[aymanadel]

I wish I could see at least one of my instructors explaining like you. You are the best that I have never seen. Break a leg.

[husseinshimal]

Your voice makes this easy to understand. Thank you

[LateNightRituals]

best thing that has ever happened to youtube. thank u

[rajendramisir]

I like the patience and tenacity with which you explain how to evaluate this line integral example. You derived the first order parametric equations for each of the 3D coordinates well. I would like to see examples of line integrals of vector and scalar fields - such as work done by a vector field along a curve from point a to point b.

[siddhant.u]

One picture is worth than million words!!, its proved by your lectures
thank you for your contribution to education
great job and keep it up!

[chetanasingh]

I never understood this concept so well before...you have an amazing voice and the way you explain things looks so simple!! Thanks a ton...keep uploading more... :)

[arvincunningham]

You are awesome when it comes to this calculus thing! I went through this semester without the aid of your videos much, and wish I had spent more time on those topics covered with the aid of your videos. Again Thank you for your time and efforts to place this information out where struggling students like myself can access it!

[ptyptypty]

OMG.. I just started this Video and I'm at the 53 second mark ... and I had to Stop the Video so I could Post a comment!.. This Video is EXACTLY what I've been looking for!!.. THANK YOU KRISTA!!.. YOU're more of a QUEEN than a KING.. (doesn't the Queen have more power in Chess?) :D.. THANK YOU... I must have wasted 2 hours going through OTHER videos trying to figure out the Intuition of the LINE Integral.. and well.. I guess Fate saves the Best for LAST.. thank you Krista!!.. and depending on when you read this.. Merry Christmas.. :) ..

[firstdbzmaker]

when t=0, f is at the starting point of the curve (0, 0, 0)
when t=1, f is at the end point of the curve (1, 2, 3)
so when you put from t=0 to t=1 into the parametric equations, you will have precisely the curve (line segment) described in the problem.

Pretty much, we choose to parameterize from t=0 to t=1 to keep the integral simple.

[jesroe]

Thank you. May you be blessed with many views and subscribers

[erichendricks]

Great job explaining what a Line Integral actually represents with your picture. Very helpful!

[pattymckenna]

A comment regarding interpretation. The function w=f(x, y, z) is in 4space, so it can’t be drawn as a curve in 3space.
Instead, I would suggest interpreting the function f with 3 independent variables and a fourth, dependent variable as a linear density function, imagining that the density of the material that makes up the line segment (think “wire”) varies, depending on the spot. The units on the linear density function f (the integrand before the “ds”) would be something like “grams per centimeter”. The symbol “ds” represents a tiny length of the wire (units: cm). When these get multiplied, we see that the integral is adding up “grams”, to find total mass of the “wire” (line segment) of variable density.

[mariahslittlelamb]

love how straight to the point you are <3

[bryanwills]

brilliant, what a great job of explaining all the steps

[haimbenavraham]

Now you understand why math is called the Queen of the Sciences. She's more artistic than the other guys.

[kimtaeyeonismyeverything]

Saving my butt from one math class to the next i swear to god 😭 thank you!!!!

[annl]

More helpful than my teacher! Thank you