# 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.

Source: https://practicecalculus.com/courses/mcgill-math-141
Updated: 2026-11-03

## 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](/learn/calculus-1/integrals/undoing-derivatives) and [Calculus 2](/learn/calculus-2)

## Key takeaways

- McGill MATH 141 is a 4-credit Calculus 2 course that follows MATH 139, 140 or 150.
- It covers the definite integral, integration techniques and applications, then introduces sequences and series.
- It is offered in summer, fall and winter.
- After MATH 141, students continue to MATH 222, Calculus 3.

**MATH 141** is Calculus 2 at McGill University, the second course in the main calculus sequence after [MATH 140](/courses/mcgill-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](/courses/mcgill-math-222), whose topics start with Taylor series.

## MATH 141 topic map

| MATH 141 topic | Practice | Read |
| --- | --- | --- |
| Riemann sums | [Area with rectangles](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| The definite integral and FTC | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus), [definite integral properties](/rules/definite-integral-properties) |
| Substitution | [U-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution](/blog/u-substitution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts](/blog/integration-by-parts) |
| Trig integrals and trig substitution | [Powers of sine and cosine](/learn/calculus-2/integration-techniques/trig-integrals) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Applications: area and volume | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves), [volumes of revolution](/blog/volumes-of-revolution) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Sequences | [Sequences and their limits](/learn/calculus-2/sequences-and-series/sequences) | [Squeeze theorem](/theorems/squeeze-theorem) |
| Introduction to series | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Geometric series](/blog/geometric-series), [convergence tests](/blog/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](/courses/mcgill-math-140) | Calculus 1 | 3 | Limits, derivatives, antiderivatives |
| MATH 141 | Calculus 2 | 4 | Definite integral, techniques, applications, sequences and series |
| [MATH 222](/courses/mcgill-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 $u = \ln x$, $dv = dx$:

$$\int \ln x\,dx = x\ln x - \int x \cdot \frac{1}{x}\,dx = x\ln x - x + C$$

**2. Area between curves.** The curves $y = x$ and $y = x^2$ meet at $x = 0$ and $x = 1$, with $x$ on top:

$$\int_0^1 (x - x^2)\,dx = \frac{1}{2} - \frac{1}{3} = \frac{1}{6}$$

**3. A telescoping series.**

$$\sum_{n=1}^{\infty} \left(\frac{1}{n} - \frac{1}{n + 1}\right) = \lim_{N \to \infty}\left(1 - \frac{1}{N + 1}\right) = 1$$

## How to do well in McGill MATH 141

- **Train your technique choice.** The [choosing a strategy](/learn/calculus-2/integration-techniques/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](/formulas) lists the standard integrals in one place.
- **Practice mixed sets.** Exams mix techniques, so mixed, timed [practice](/practice) sets prepare you better than drilling one method at a time. The [common calculus mistakes](/blog/common-calculus-mistakes) guide shows what to watch for.

> **Tip:** for series, always check the [nth-term test](/rules/nth-term-test) first. If the terms do not go to zero, the series diverges and you are done.

## Frequently asked questions

### What is McGill MATH 141?

MATH 141 is Calculus 2 at McGill. It covers the definite integral, techniques of integration, applications of integration, and an introduction to sequences and series.

### What do I need before MATH 141?

One of MATH 139, MATH 140 or MATH 150. Students with CEGEP objective 00UP or an equivalent already have credit for this material and cannot take it.

### Is McGill MATH 141 hard?

Many students find it harder than MATH 140, because integration needs strategy and series are a new way of thinking. Practicing integration techniques until you can recognize which one to use is the most effective preparation.

### What comes after MATH 141?

MATH 222, Calculus 3, which needs MATH 141 plus familiarity with vector geometry or MATH 133 taken at the same time.

### MATH 141 vs MATH 151: what is the difference?

MATH 151, Calculus B, follows MATH 150 and covers integration, series, power series, arc length, curvature and multiple integration. MATH 150 and 151 together cover what MATH 140, 141 and 222 cover, so MATH 151 is the faster route for strong students.