United University

Algebra Grade 11. Integral and its applications. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 16 hours

This course helps students master the fundamentals of integral calculus and its practical applications: the concept of antiderivatives, rules for computing integrals, definite integrals, and calculating the areas of curved trapezoids and plane figures.

The course includes interactive tests with automatic grading, homework assignments, and review exercises that allow students to reinforce their knowledge in practice. Learners develop logical thinking, problem-solving skills, and the ability to apply mathematical concepts in real-life contexts.

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Master the art of integration with confidence! Our "Algebra Grade 11. Integral and its applications. Collection 1" course guides students through the foundational and practical aspects of integral calculus. Learners will explore definitions, fundamental properties, and key formulas of antiderivatives, as well as the concept and applications of definite integrals for calculating areas of curved trapezoids and plane figures.

Why choose our course:

  • Comprehensive structure: The course includes theory, step-by-step examples, interactive exercises, and automatic knowledge checks.
  • Curriculum alignment: Fully corresponds to the State Standard of Basic Secondary Education and model programs for Grade 11.
  • Practical applications: Learn to compute integrals, determine areas, and interpret results through real-life mathematical contexts.

Course Modules

Module 1: Exponential and logarithmic functions

Module 2: Integral and its applications

  • §11. Antiderivative and its properties
  • §11. Antiderivative and its properties (Part 1)
  • §11. Antiderivative and its properties (Part 2)
  • Knowledge check for §11
  • §12. Table of antiderivatives. Rules for finding antiderivatives
  • §12. Table of antiderivatives. Rules for finding antiderivatives (Part 1)
  • §12. Table of antiderivatives. Rules for finding antiderivatives (Part 2)
  • §12. Table of antiderivatives. Rules for finding antiderivatives (Part 3)
  • Knowledge check for §12
  • §13. Definite integral: physical and geometric meaning
  • §13. Definite integral: physical and geometric meaning (Part 1)
  • §13. Definite integral: physical and geometric meaning (Part 2)
  • Knowledge check for §13
  • Homework assignment №4
  • Knowledge check tasks for §§11–13
  • §14. Calculating definite integrals. Basic properties of definite integrals
  • §14. Calculating definite integrals. Basic properties of definite integrals (Part 1)
  • §14. Calculating definite integrals. Basic properties of definite integrals (Part 2)
  • Knowledge check for §14
  • §15. Calculating areas of plane figures and other applications of the integral
  • §15. Calculating areas of plane figures and other applications of the integral (Part 1)
  • §15. Calculating areas of plane figures and other applications of the integral (Part 2)
  • §15. Calculating areas of plane figures and other applications of the integral (Part 3)
  • Knowledge check for §15
  • Homework assignment №5
  • Knowledge check tasks for §§14–15
  • Revision exercises for Module 2 (for §§11–12)
  • Revision exercises for Module 2 (for §§13–14)
  • Revision exercises for Module 2 (for §15)
  • Ukrainian Women in the World

Expected Learning Outcomes

  • Find antiderivatives using the table of antiderivatives and their properties.
  • Identify antiderivatives satisfying given initial conditions.
  • Compute integrals using fundamental rules and formulas.
  • Understand and apply the geometric and physical meanings of definite integrals.
  • Calculate areas of curved trapezoids and plane figures.
  • Develop logical thinking, problem-solving skills, and the ability to apply mathematical concepts in real-life contexts.

By the end of this course, students will have a solid understanding of integral calculus, the ability to compute definite and indefinite integrals, and the skills to apply these concepts in geometry and physics, preparing them for advanced studies and academic success.

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