What is integral? What is formula for integral? When do students in Vietnam learn about integral according to Mathematics curriculum in Vietnam?
What is integral? What is formula for integral?
Integral is a more complex mathematical concept than differentiation. Integral is the inverse operation of differentiation. While differentiation gives us the rate of change of a function at a specific point. Integral helps us find the original function given its rate of change.
| Integral Formulas Integral formulas are a crucial tool in mathematics, particularly in calculus. They help us calculate areas, volumes, arc lengths, and many other quantities related to functions. Basic Formula: The definite integral formula of a function f(x) over the interval [a, b] is defined as follows: ∫[a, b] f(x) dx = F(b) - F(a) Where: ∫: Integral symbol [a, b]: Integral interval f(x): Function to be integrated F(x): Antiderivative of f(x) (meaning F'(x) = f(x)) dx: Denotes the variable of Integral Geometric Meaning: Area: The definite integral gives us the area of the plane figure bounded by the graph of the function y = f(x), the x-axis, and the two vertical lines x = a and x = b. Methods of Calculating Integrals: Integral by parts: Used to integrate the product of two functions. Change of variable: Used to transform the integral into a simpler form. Integral of trigonometric functions: There are specific formulas for functions like sin, cos, tan,... Integral of rational functions: Uses partial fraction decomposition. Some common Integral formulas: Integral of exponential functions: ∫e^x dx = e^x + C Integral of power functions: ∫x^n dx = (x^(n+1))/(n+1) + C (with n ≠ -1) Integral of trigonometric functions: ∫sin(x) dx = -cos(x) + C ∫cos(x) dx = sin(x) + C |
*Note: Information is for reference purposes only./.
What is integral? What is formula for integral? When do students in Vietnam learn about integral according to Mathematics curriculum in Vietnam? (Image from the Internet)
When do students in Vietnam learn about integral according to Mathematics curriculum in Vietnam?
Based on Section V of the Mathematics Curriculum, issued together with Circular 32/2018/TT-BGDDT, the evaluation of grade 12 Mathematics is stipulated as follows:
As per the distribution of the content strands across grades, integral will be taught in the Grade 12 Mathematics program.
What are objectives of grade 12 mathematics in Vietnam?
Based on subsection 3 of Section III of the Mathematics Curriculum, issued together with Circular 32/2018/TT-BGDDT, the assessment of grade 12 mathematics will comply with the following methods:
The upper secondary school mathematics course aims to help students achieve the following main objectives:
- Contribute to the formation and development of mathematical competence with the following requirements to be achieved:
+ Ask and answer questions when reasoning and solving problems; use argumentative, inductive, and deductive methods to understand different ways of solving problems; establish mathematical models to describe situations, thereby proposing solutions to mathematical problems presented in the established model;
+ Implement and present problem-solving solutions and evaluate implemented solutions, reflecting on the value of the solution, generalizing for similar problems;
+ Use tools and means to learn, explore, and solve mathematical problems.
- Have basic and essential mathematical knowledge and skills regarding:
+ Algebra and Some Analytical Elements: Calculation and use of computational tools; use of algebraic languages and notations; transformation of algebraic and transcendental expressions (trigonometric, exponential, logarithmic), equations, systems of equations, inequalities; recognition of basic elementary functions (power, trigonometric, exponential, logarithmic); study of functions and graph plotting using derivatives; use functions language, function graphs to describe and analyze some processes and phenomena in the real world; use integrals to calculate planar areas and volumes of objects in space.
+ Geometry and Measurement: Provide knowledge and skills (at logical reasoning level) about geometric relationships and familiar plane and solid shapes; algebraic methods (vector, coordinate) in geometry; development of spatial imagination; solving simple practical problems associated with Geometry and Measurement.
+ Statistics and Probability: Complete the ability to collect, classify, represent, analyze, and process statistical data; use statistical data analysis tools through characteristic numbers measuring central trend and dispersion level for grouped and ungrouped data samples; use statistical laws in practice; recognize random models, basic probability concepts and the significance of probability in practice.
- Contribute to providing students with a relatively comprehensive understanding of careers associated with mathematics and its value; serve as a basis for post-secondary career orientation; have minimum capacity to self-explore issues related to mathematics throughout life.
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