MAT1575: Calculus 2

Instructor: Suman Ganguli | Fall 2023

Page 9 of 12

Integration by Substitution: HW + Videos

I uploaded a pdf with homework exercises on integration by substitution to Files. I will also provide hard copies of this in class tomorrow, and we will go through some similar examples. This homework is due in one week, on Wed Oct 4. I will also assign a WebWork set on this topic.

You may find these videos helpful for learning integration by substitution:

“Integration using U-Substitution”: https://youtu.be/qclrs-1rpKI

Those 3 videos are from a YouTube math channel called PatrickJMT. You can find his playlist for integral calculus here. We will be covering most of those topics this semester, so you may want to revisit that playlist over the course of the semester.

If you prefer Khan Academy, see these videos in their calculus course. In particular, here is Khan Academy’s playlist on substitution, which starts with the following video:

Class 7 Recap (Wed Sept 20)

Class Info

  • Date: Wed, Sept 20
  • Meeting Info: 10a-11:40a, N719

Announcement

The college is closed on Monday (Sept 25), so our next class meeting will be next Wednesday (Sept 27). Please complete the open WebWork set in the meantime:

“Integration – Fundamental Theorem constant bounds” (due Mon Sept 25)

“Review – Chain Rule” (due Wed Sept 27)

In addition, I will post a written HW set on integration by substitution (see below).

Topics

Integration by substitution (see Sec 1.5 – Substitution):

To-Do After Class

  • Continue working on “Integration – Fundamental Theorem constant bounds” (due Mon Sept 25) and “Review – Chain Rule” (due Wed Sept 27)

Class 6 Recap (Mon Sept 18)

Class Info

  • Date: Mon, Sept 18
  • Meeting Info: 10a-11:40a, N719

Announcement

We will have our first quiz at the end of class on Wednesday (tomorrow). It will consist of one or two exercises similar to the exercises in “Integration – Definite Integrals”, i.e, calculating a definite integral of a given linear function over a given interval using area calculations. There will also be a simple application of the Fundamental Theorem of Calculus to calculate the same definite integral.

Topics

Examples from “Integration – Fundamental Theorem constant bounds”:

Reviewed differentiation using the Chain Rule, in order to introduce integration by substitution (see Sec 1.5 – Substitution):

To-Do After Class

  • Continue working on “Integration – Fundamental Theorem constant bounds” (due Mon Sept 25) and “Review – Chain Rule” (due Wed Sept 27)
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