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    In mathematics, the calculation of volume is an indispensable part. However, in real-life construction and various productions, the volume we require to calculate cannot be simply calculated like: long * width * high. So for all kinds of odd-shaped parts, if we want to know its volume (for example, how much material is needed to make a certain item), one of the ways is to divide it into many small cross-sections and perform step-by-step calculations ( You can also put it directly into a container filled with water, and then look at the volume of water discharged, I think this method is simpler, but not everything can be put in the water, is’t it?).

    To give a very simple example, to calculate the volume of a dumpling, direct calculation may not be very simple, but we can divide it into many parts longitudinally, so that each part looks like a triangle. By calculating the volume of each part, Then add up to get a relatively accurate value. The more data points, the closer to the real volume.
    I used two simpler equations: y=0.5\sin x and y=-0.5\sin x, They can intersect a lot of "dumplings"
    The intersection of the two functions is at (kπ, 0), k ∈ 整数集. So We take out one of the "dumplings":
    Then its overall length is from (0, 0) to (π, 0), we divide it into 15 parts to calculate, assuming that the cross section of each part is a regular triangle. The height of each serving is 0.20943.


    Modeling through these data, we can get this

    We add up all the volumes and we can get that the volume of "dumplings" is about 1.36026.
    
    So, next calculate the real volume of this "dumpling", we use the function 
∫ (0.5sinx-(-0.5sinx))*(sinπ/3)*(0.5sinx-(-0.5sinx))dx from 0 to π to calculate, The function in the middle can be simplified to sinx*sinx*(sinπ/3). After calculation, the final score is 1.36034. The two scores are very close. This is a very simple and easy to show example. Relatively speaking, it is also a special but very common Chinese food, so I hope it will help to understand this method.
    
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