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Integral calculation

Course Description: Fundamental theory of differential and integral calculus, definite and indefinite integrals. Area, volume of revolution, work, arc length. Integration of inverse trigonometric, logarithmic, exponential, hyperbolic, and inverse hyperbolic functions. Techniques of integration: substitution, parts, trigonometric substitution, partial fractions, miscellaneous substitutions. Numerical integration, improper integrals. Parametric and polar curves.
Credit hours: 3
Prerequisites: MATH105
Objectives of the course :

The goal of this module is to:
Familiarity with the concept of integral calculus and its applications.
(B) Understand the fundamental techniques for solving various types of engineering and science problems.
(C) Explain the properties of integral calculus and techniques of integration.
(d) Explanation of logarithmic, exponential, inverse, and hyperbolic functions.
(h) Numerical integration calculation using the trapezoidal rule and Simpson's rule.
Understanding how to calculate area, volume, surface area, and arc length.

Course outputs :
  • Define definite and indefinite integrals, then find them.
  • The Fundamental Theorem of Calculus, and the Mean Value Theorem for a function.
  • Find the integrals involving logarithmic functions, exponential functions, trigonometric functions, inverse trigonometric functions, and hyperbolic functions and their inverses.
  • Describe the methods of integration by parts, trigonometric substitution, and partial fractions.
  • Define improper integrals, then evaluate them.
  • Parametric equations, tangent lines, and arc length of parametric curves, and polar coordinates.
  • Evaluate integration by parts, and use trigonometric substitution to evaluate integrals.
  • Calculate the area between two curves, and the arc length for both parametric and nonparametric curves.
  • Calculate the volume and surface area of the solid of revolution, and the work.
  • Calculate the integral of rational functions using partial fractions and indefinite integrals.
  • Numerical integration using the trapezoidal approximation, Simpson's rule.
Additional information:
  • Last updated: 2026-05-17

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