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Week 4, Short Day: Integration Techniques

Whether we have to determine single integrals, double integrals or triple integrals we usually end up having to compute single integrals in any case, maybe several times, as you know them from highschool. First you must find an indefinite integral and then insert the integral limits. But finding indefinite integrals can be rather tricky, sometimes even impossible! Today we will train integration techniques.

Today’s Key Concepts

Indefinite versus definite integral. Partial integration. Integration by substitution. Line integral.

Preparation and Syllabus

Again today our material is eNote 23 Riemann Integrals and we continue browsing through eNote 24 Line and Plane Integrals for useful tools for curve parametrization.

Activity Program

  • 13:00 – 14.00: $\,$ Lecture (aud. 42, b. 303A) (link to streaming)
  • 14.00 – 16.00: $\,$ Group exercises in the study areas (b. 302, bottom floor)
  • 16.00 – 17.00: $\,$ Weekly test

Group Exercises

  1. Definite Integrals
  2. Integration by Parts. By Hand
  3. Integration by Substitution
  4. Parametrization and Line Integral. By Hand
  5. Area and Volume. Advanced

Weekly Test

For all Weekly Tests, the following applies:

  • The test is an on-location test, meaning it can only be accessed in the study area.
  • No electronic aids are allowed (except for your own notes on e.g. a tablet).
  • The test can be accessed in the Möbius quiz system via a link on DTU Learn in the module for 01006 (in the top menu click “Möbius”).
  • Your solutions to the test questions must be typed into Möbius without in-between calculations or steps. The result is automatically evaluated by Möbius.
  • To ensure a smooth experience use the Firefox or Chrome browser, and disable any add-blocker.
  • Use a DTU network.
  • You may discuss the test questions with fellow students in your study group, but you have your own version of the test with scrambled numbers that you yourself must solve and enter into Möbius.
  • During the final hour on Fridays you have one attempt. Passing this attempt will grant you 1 bonus point. From Friday at 18:00 until Wednesday at 18:00 the test is reopened for repeated attempts. Passing during this phase will grant you ½ bonus point.