McGill MATH 141 Calculus 2: Topics, Study Guide and Practice
A study guide for McGill MATH 141 (Calculus 2): the definite integral, integration techniques, applications, sequences and series, with practice.
McGill University Updated 3 min read
At a glance
- Course code
- MATH 141
- Credits
- 4
- Offered
- Summer 2026, Fall 2026 and Winter 2027
- Prerequisites
- MATH 139, MATH 140 or MATH 150
- Restrictions
- Not open to students who have taken CEGEP objective 00UP or equivalent, or (except by permission) MATH 122
- Covers
- The definite integral, techniques of integration, applications, and an introduction to sequences and series
- Next course
- MATH 222 (Calculus 3)
- Practice here
- Calculus 1 integrals and Calculus 2
On this page
MATH 141 is Calculus 2 at McGill University, the second course in the main calculus sequence after MATH 140. It begins with the definite integral, spends most of the term on integration techniques and applications, and finishes with an introduction to sequences and series. This guide maps each MATH 141 topic to practice so you can learn integration one problem at a time.
What McGill MATH 141 covers
McGill's Department of Mathematics and Statistics lists the topics as the definite integral, techniques of integration, applications, and an introduction to sequences and series. The course is worth 4 credits and runs in summer, fall and winter.
That lines up with the integral half of a standard Calculus 1 course plus the main part of Calculus 2. Since the description says "an introduction" to sequences and series, the deeper treatment of power and Taylor series continues in MATH 222, whose topics start with Taylor series.
MATH 141 topic map
| MATH 141 topic | Practice | Read |
|---|---|---|
| Riemann sums | Area with rectangles | Riemann sums |
| The definite integral and FTC | Evaluating definite integrals | Fundamental Theorem of Calculus, definite integral properties |
| Substitution | U-substitution | u-substitution |
| Integration by parts | Integration by parts | Integration by parts |
| Trig integrals and trig substitution | Powers of sine and cosine | Trig substitution |
| Partial fractions | Partial fractions | Partial fractions |
| Applications: area and volume | Area between curves | Area between curves, volumes of revolution |
| Improper integrals | Integrating to infinity | Improper integrals |
| Sequences | Sequences and their limits | Squeeze theorem |
| Introduction to series | Geometric series | Geometric series, convergence tests |
The listed description names techniques of integration and applications without itemizing them, so the technique and application rows above are the ones a typical Calculus 2 course includes.
MATH 141 in McGill's calculus sequence
| Course | Title | Credits | Content |
|---|---|---|---|
| MATH 140 | Calculus 1 | 3 | Limits, derivatives, antiderivatives |
| MATH 141 | Calculus 2 | 4 | Definite integral, techniques, applications, sequences and series |
| MATH 222 | Calculus 3 | 3 | Taylor series, partial derivatives, multiple integrals |
| MATH 151 | Calculus B | 4 | Faster alternative after MATH 150 (not offered this catalogue year) |
Example problems at the MATH 141 level
1. Integration by parts. Evaluate \int \ln x\,dx with u = \ln x, dv = dx:
2. Area between curves. The curves y = x and y = x^2 meet at x = 0 and x = 1, with x on top:
3. A telescoping series.
How to do well in McGill MATH 141
- Train your technique choice. The choosing a strategy lesson teaches you to spot substitution, parts or partial fractions quickly.
- Draw before you integrate. Sketch every region for area and volume questions to get the right limits and the right top curve.
- Keep a formula sheet. The calculus formula sheet lists the standard integrals in one place.
- Practice mixed sets. Exams mix techniques, so mixed, timed practice sets prepare you better than drilling one method at a time. The common calculus mistakes guide shows what to watch for.
Tip: for series, always check the nth-term test first. If the terms do not go to zero, the series diverges and you are done.
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Area with rectangles
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