I am having a bit of difficulty understanding the intuition behind it. So here my understanding so far, I have attached some photos of the book I am using to understand integration.(adsbygoogle = window.adsbygoogle || []).push({});

This is from the book I have posted, I am just going up to the part I do not understand.

S basically I have to consider a rectangle ( which is the one at the bottom of the first photograph ). This rectangle has a width of δx. An area of δA which is the shaded area.

The area of rectangle ABEF is yδx: which is pretty self explanatory.

The area of rectangle ABCD is (y+δy)δx

Therfore we have: yδx<δA <(y+δy)δx: So all this is doing is comparing the area to the 2 rectangles

Now the confusion begins, it say beceause δx >0 You should divided through by. Why is this?

Letting δx [itex]\rightarrow[/itex]0 gives [itex]\frac{δA}{δx}\rightarrow\frac{dA}{d} [/itex] and δy[itex]\rightarrow[/itex]0 therefore [itex]\frac{dA}{dx}=y[/itex] this to me is saying that x is the independent variable and δA dependent variable; correct? So as more rectangle are add then obviously the area will get smaller and the more rectangles add δy will reach zero. But how dose [itex]\frac{dA}{dx}=y[/itex]

This is the trouble I am having up to a point, if someone could ans and the I will ask the other half of the trouble I am having. Or if someone feel like it explain from the beginning how the intergration of the curve works.

I am new to integration so I would appreciate all the help anyone can offer.

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# Understanding the area under a curv and trapizum rule

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