How to Calculate Arc Length Using Integration?

by Oliver Mark on Jan 7, 2019 97 Views

What is integration?

Integration is a part of calculus in which smaller components are grouped together to form a single system. Small slices of a line or arc are calculated in order to calculate the whole. The smaller the slices, the more accurate the value will be. An integral is the reverse of finding a derivative. Integration is just like filling up a large tank through a small tap. The input we get before integration will be the rate of flow from the tap. Now integrating the flow i.e. adding the little drops of water can determine the volume of the water in the tank.

How it is used to calculate arc length?

By using Integration we can very easily calculate the length of an arc. First we will divide the length of the curve into infinitely small parts. Then we figure out length of each small part and then add up all the small lengths. When we zoom and see a curve, its length seems to be the hypotenuse of a right angled triangle. So, by calculating the lengths of all hypotenuses from starting up to the finishing point we come to the actual length of the arc or curve.

Let us take the two sides of right angled triangle (obtained by zooming the curve) i.e. base and height as dx and dy. Then according to the Pythagoras Theorem, the length of hypotenuse is

The expression given inside this integral is simply the length of the representative hypotenuse of the right angled triangles.

Thus, we can see that through the use of integration we can easily calculate the length of curved surfaces. This is very essential for the civil and mechanical engineers. The construction of roads, their slopes and all difficult terrains can be handled with integration. In mechanical engineering integration forms an inseparable part of this discipline as it helps in designing tools and instruments needed in mechanics. All such assignments are being categorized under arc length Assignments. BookMyEssay can be your right partner for arc length Assignment Help.

BookMyEssay is a well known online professional assignment help provider. Based in Australia, it is the most popular assignment help among the students across the world. Calculus assignments and specially arc length assignments through integration are its best offers to the students of mathematics. Our writers are proficient in integration and provide world class arc length assignment help to the students. All this is available at very reasonable rates.

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