Tài liệu toán viết bằng tiếng anh | Môn toán cao cấp

lOMoAR cPSD| 49519085
1/ Website co-founder team
First and foremost, we, the two co-founders of the website "pioneers of creativity," would like
to thank you for visiting our website.
Allow us to introduce our information next so that you may grasp it better. We are a group of
Ho Chi Minh City University of Law students studying Business Administration - Law. We
established this website to learn calculus in general and integral in specific in order to provide
everyone with knowledge about advanced math. The information on this page is based on our
study and references in other documents.
Finally, we hope you enjoy and learn from your visit to our website. Please provide us feedback
through email if you run across technical issues when exploring the information we provide or
find that it is inaccurate.
2/ What is integral?
Acording to Wolfram MathWorld, the term "integral" can refer to a number of different
concepts in mathematics. The most common meaning is the the fundamenetal object of
calculus corresponding to summing infinitesimal pieces to find the content of a continuous
region. Other uses of "integral" include values that always take on integer values (e.g., integral
embedding, integral graph), mathematical objects for which integers form basic examples
(e.g., integral domain) and particular values of an equation (e.g., integral curve) 2/ How
many types of integral? -
Indefinite Integrals: It is an integral of a function when there is no limit for
integration. It contains an arbitrary constant. -
Definite Integrals: An integral of a function with limits of integration. There are two
values as the limits for the interval of integration. One is the lower limit and the other is the
upper limit. It does not contain any constant of integration.
3/ Applications of Integrations
We all undoubtedly learn about calculus in general and integration in particular when
attending school. So, have you ever questioned what use those intricate formulae and
challenging puzzles are to us? And is there any practical use for it in professional or everyday settings?
If you are unaware of these fascinating applications, allow us to provide you this knowledge
about them. Alternatively, if you already have a solid grasp on integrals, come learn more about this topic with us.
- In Mathematics integrals are used to find: lOMoAR cPSD| 49519085
• Center of mass (Centroid) of an area having curved sides
• The average value of a curve
• The area between two curves
• The area under a curve
- In Physics integrals are used to find: • Centre of gravity • Center of mass
• Mass and moment of inertia of vehicles
• Mass and momentum of satellites
• The velocity and trajectory of a satellite • Thrust
- In real life:
1. Calculating pressure within damage
Let us consider a dam. When the reservoir behind it is full, the dam withstands a great deal of
force. We can use integration to calculate the force exerted on the dam when the reservoir is
full and also calculate how changing water levels affect that force. Hydrostatic force is one of
the many applications of integrals. 2. Automobiles
In an automobile, we always find an odometer and a speedometer. Their gauges work in
synchrony and determine the speed and distance the automobile has traveled. The electronic
meters use differentiation to transform the data sent to the motherboard from the wheels
(speed) and the distance (odometer). 3. Business
One of the most common applications of derivatives of differentiation is when data is
computed on a graph or a data table like an Excel sheet. Once there is an input, one can
calculate the profit or loss by means of derivatives. 4. Astronomy
Space flight engineers frequently use calculus when planning lengthy missions. To launch a
rocket, calculus allows each of those variables to accurately take into account the orbiting
velocities under the gravitational influences of the sun and the moon. This is one of the most
crucial instances of real-life applications of differentiation. lOMoAR cPSD| 49519085 5. Economics
Differential calculus is used in economics to calculate marginal cost, marginal revenue,
maxima, and minima, and also enables economists to predict maximum profit (or) minimum
loss in specific conditions. 6. Swimming pools
Integration determines the amount of water used to fill a swimming pool. We first need to
determine the shape of the swimming pool and find its size. Therefore, we find the amount of
water that will fill it. If the swimming pool shape is not a regular geometric shape, it begins with a slight gradient.
After which the slope descends steeply. The sides of the pool are either curved or semielliptical.
The surface also has rises and falls. In such a case, it is possible to find the volume by using
integration, which helps find the area between curved surfaces. 8. Medicine
Calculus is a crucial mathematical tool for analyzing drug activity quantitatively. Differential
equations are utilized to relate the concentrations of drugs in various body organs over time.
In addition, integrated equations are often used to model the cumulative therapeutic or toxic
outcomes of drugs in the body. 9. Architecture
Calculus can be used by architects to express design plans through graphs or drawings. They
can describe surfaces through maths to help adapt the drawing to the computer software.
This can be done through various differential equations. Calculus was used in the designing
and construction of the Eiffel tower. 10. Credit card
Companies use differential calculus to calculate the minimum payable amount. There are
several variables that go into this calculation. It is calculated by the amount of money that is
due by the due date. The rate of interest also needs to be considered. With all these changing
values, interest rates, and account balances, the calculation has to be done simultaneously in
order to provide the customer with an accurate minimum balance and amount payable.
In conclusion, calculus is a mathematical idea that is frequently applied in mathematical
models to obtain the best results and aids in comprehending changes in the values related to a
function. The ideas of difference and integration also have a big impact on our lives without
us even realizing it. They are connected to practically every aspect of life, including math,
science, and economics. Differentiation and integration are crucial concepts in the real world
as well as a branch of mathematics. lOMoAR cPSD| 49519085
Calculus is the foundational course for anyone pursuing careers in math or science because of
its wide range of applications.
https://www.cuemath.com/calculus/applications-of-integrals/
https://www.vedantu.com/maths/application-of-integrals
https://numberdyslexia.com/applications-of-integration-and-differentiation-in-real-life/