Motivation of integration
Integration is used to calculate the area under a certain line, curve or the area which covered by an image in math. Like calculating the area for a piece of leaf. When we doing integration, we separate the leaf to a lot small rectangle strips whose area can be easily calculated. Approximately, the sum area of strips is area of the leaf. Moreover, integration can be used to calculate a curve’s length by regarding the curve to a lot short straight lines. As an important math concept, not only can it be applied in math to calculate area and length and in physics to calculate the movement about one subject, it can also be applied in our daily life observation.
It was a sunny day, our team was eating in the Orchard Common, and we found it that there is a big irregular hole (the depth varies) on the table. Everyone wanted to know the exact volume of plastic material do the staff in dining hall need to fill this hole. At the same time, Tracey was eating French Fries, she was thinking “Oh why not fill the hole with fries so as to calculate the volume by calculating the volume of fries?”. It is noted that French Fries has the same length and width but different height and the height of fries could be cut to fit the depth of the hole.
To calculate the volume of the hole, firstly we put a cardboard under the hole so as to accommodate the fries in case they fell on the ground. And then the filling started from the side of the hole. We put fries into the hole and compared the height between the fries and the depth of the hole. The extra parts were eaten by Tracey. And repeat the procedure. Finally, the irregular hole was full. Now Tracey put all the fries from the hole on the plate in order. Vivienne yelled that, it is the volume of the hole, we can calculate the total volume by adding the volume of fries one by one. It’s obvious that the volumes of different fries are easy to calculate once knowing the fixed length & width and the various heights. This is a normal case in daily life.
Like the volume of a hole we saw in our dining hall. We can separate it in small pieces and get the hole’s volume by calculating every small piece’ volume. The method is just the basic content of integration. Integration, in total, is a method to make complicate things easier by making it smaller. Thinking of puzzles, every little piece of puzzle can be connected together to a masterpiece. By using the way to integrate something, we can approximately get the value which is hard to get straightly.
teammates: Mengmeng Li (Astrid) 59418160
Jingwen Bai (Vivienne) 55932164
Cuishan Xu (Tracey) 32182164
Xuechun Lu(Leonie) 41519166