What is Strips in Calculus?

Let's say I have a graph. I break that graph up into tiny rectangles with a infinitesimal small width

\delta x

and height equal to the f(x). And then add the areas of the rectangles up. This is strips method of integration right?

Reply 1

username4626084

Derivation is like cutting the graph into pieces, while Integration is collecting and adding all these pieces. So if you wanna get the area under any curve, you integrate the equation of the curve which is given as f(x) or whatever you name it. Derivation is used to cut the graph into pieces to study many stuffs on the graph. Some of these things are the minima and maxima, critical point etc..

Reply 2

mqb2766

Yes.

Original post by esrever

Let's say I have a graph. I break that graph up into tiny rectangles with a infinitesimal small width

\delta x

and height equal to the f(x). And then add the areas of the rectangles up. This is strips method of integration right?

Reply 3

AirMarshal

What you've described is called Integration from First Principles... As the delta-x becomes infinitely small, it becomes dx, resulting in your standard Leibniz notation for calculus

Original post by esrever

Let's say I have a graph. I break that graph up into tiny rectangles with a infinitesimal small width

\delta x

and height equal to the f(x). And then add the areas of the rectangles up. This is strips method of integration right?

Reply 4

esrever

Original post by HydraFly

What you've described is called Integration from First Principles... As the delta-x becomes infinitely small, it becomes dx, resulting in your standard Leibniz notation for calculus

Original post by mqb2766

Yes.

Thanks. But is this method known by a name other than "strips"? Because I was unable to find any information about it online.

Reply 5

AirMarshal

Yes... Its called integration from first principles! Here's a link: Here!

Alternatively, if you are not making the strips infinitely small but just extremely narrow, it becomes an approximation technique called 'the trapezium rule' - except you use trapeziums instead of rectangles as this gives a better approximation.

Original post by esrever

Thanks. But is this method known by a name other than "strips"? Because I was unable to find any information about it online.