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Integral Calculus

Rakennetyyppi: Opintojakso
Koodi: IITB3005
OPS: IT 2021
Taso: Insinööri (AMK)
Opiskeluvuosi: 2 (2022-2023)
Lukukausi: Kevät
Laajuus: 2 op
Vastuuopettaja: Mäkelä, Jarmo
Opetuskieli: Englanti

Toteutukset lukuvuonna 2022-2023

3003IT2021-2, IT2021-2A, IT2021-2B9.1.2023 – 25.3.2023Jarmo MäkeläEnglanti1.12.2022 – 9.1.2023


The integral of a function gives an answer to the question: Which is the function, whose derivative the given function is? For example, (one of) the integral function(s) of 2x is x^2, since the derivative of x^2 is 2x. The integral can be used, for example, in evaluating surface areas and volumes, and it is useful in studying the average behaviour of a function in a given time interval. In this course, the student learns to evaluate integral functions of some given functions, and she will learn how to apply integral calculus for, e.g., determining areas and volumes.

Opiskelijan työmäärä

54 h, which contains 28 h of scheduled contact studies.
The assessment of student’s own learning 1 h is included in contact lessons.


A short revision of differential calculus. The integral function. Integral function of the power function, the exponent function and the trigonometric functions. Integral of the sum. Definite integral and its interpretation as the surface area. The area enclosed by two plane curves. Integration by parts. Integration by substitution (changing the variable). Integrating a rational function by partial fractions. The average value and the root-mean-square value of a function. The length of a plane curve. The surface area and the volume of a solid of revolution. The center of mass of a homogenous planar object. Numerical integration by polynomial fitting and by Simpson’s rule.


Material prepared by the teacher.

Opetusmuoto / Opetusmenetelmät

Lectures, exercises.


Grade 5: The student is able to solve problems creatively in almost all the contents of the course.
Grade 3: The student can solve applied problems related with the central contents of the course.
Grade 1: The student can solve basic problems on the central contents of the course.


Homework exercises, assignments, an examination.