Table of Contents
- 1 How is calculus used to find the area under a curve?
- 2 Why is finding the area under a curve useful?
- 3 Why is calculus used in physics?
- 4 What does the area under the curve represent math?
- 5 What does the area under a curve represent physics?
- 6 Why is the area under the velocity curve the distance traveled?
- 7 How do you find the area under a curve?
- 8 What are the applications of calculus in science?
- 9 What is the importance of calculus in navigation?
How is calculus used to find the area under a curve?
The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b.
Why is finding the area under a curve useful?
Originally Answered: Why is it important to know the area of a curve in integral calculus? The area under a curve will indicate a number directly related to the data. Depending on the problem you are solving, it will be a solution to a question.
What is calculus used for in real life?
The most common practical use of calculus is when plotting graphs of certain formulae or functions. Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution.
Why is calculus used in physics?
In physics, for example, calculus is used to help define, explain, and calculate motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. Einstein’s theory of relativity relies on calculus, a field of mathematics that also helps economists predict how much profit a company or industry can make.
What does the area under the curve represent math?
Then the area under the whole curve is just the sum of the areas of all these tiny rectangles under the curve. Should you be interested in finding out more about this it is called Riemann integration. And velocity v times time dt is just the distance moved at a velocity v in a time dt. So the area is a distance moved.
What does the area under the curve represent physics?
The area under the curve is the magnitude of the displacement, which is equal to the distance traveled (only for constant acceleration).
What does the area under a curve represent physics?
The area under the velocity/time curve is the total displacement. If you divide that by the change in time, you will get the average velocity. Velocity is the vector form of speed. If velocity is always non-negative, then average velocity and average speed are the same.
Why is the area under the velocity curve the distance traveled?
The area under a speed-time graph is the distance. This is because speed and distance are scalars. The area under a velocity-time graph is the displacement. Velocity can be negative if an object is moving backwards.
Why do we need to study calculus?
The purpose of studying calculus is simply to introduce your mind to the scientific method of analysis. Through science, practical problems can be identified, explanations generated and logical solutions selected.
How do you find the area under a curve?
The area under the curve can be assumed to be made up of the large number of vertical, extremely thin strips. Let us take a random strip of height y and width dx as shown in the figure given above whose area is given by dA. The area dA of the strip can be given as ydx. Also, we know that any point of the curve, y is represented as f(x).
What are the applications of calculus in science?
Using calculus, scientists, astronomers, physicists, mathematicians, and chemists could now chart the orbit of the planets and stars, as well as the path of electrons and protons at the atomic level. There are two branches of calculus: differential and integral calculus.
Why do we use integral to find area under a curve?
$\\begingroup$Thanks for the explicit clarification – then why Integral is said to find area under a curve. It does means that it has more to add in its definition. Please let me know the various data we can find from Integration apart from area$\\endgroup$ – Programmer May 2 ’14 at 4:08 3
Calculus played an integral role in the development of navigation in the 17th and 18th centuries because it allowed sailors to use the position of the moon to accurately determine the local time. To chart their position at sea, navigators needed to be able to measure both time and angles with accuracy.