What is Strips in Calculus? Watch

esrever
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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?
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keptinside
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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..
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mqb2766
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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?
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HydraFly
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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?
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esrever
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(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.
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HydraFly
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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.
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Red8746
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I think the Simpsons Rule uses a similar method to what you’re describing.
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mqb2766
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Rectangular integration (as opposed to trapezoid).
Or Reimann
https://en.wikipedia.org/wiki/Riemann_sum
(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.
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graecusthegreek
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(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.
I think this is called Riemann Integration?
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esrever
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Thank you so much everyone
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