# UMD MATH141 Calculus II: Syllabus, Topics and Practice

> A study guide for UMD MATH141 Calculus II: integration techniques, improper integrals, volumes, work, exponentials, sequences and series.

Source: https://practicecalculus.com/courses/university-of-maryland-math-141
Updated: 2026-11-08

## At a glance

- **Course code:** MATH141
- **Credits:** 4
- **Prerequisites:** A minimum grade of C- in MATH140
- **Covers:** Techniques of integration, improper integrals, applications of integration (volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, sequences and series
- **Previous course:** MATH140 Calculus I
- **Next course:** MATH241 Calculus III
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH141 is the 4-credit Calculus II course at the University of Maryland, College Park, and a continuation of MATH140.
- It covers techniques of integration, improper integrals, volumes, work, arc length and moments, inverse, exponential and logarithmic functions, and sequences and series.
- The prerequisite is a minimum grade of C- in MATH140.
- A C- or better in MATH141 opens MATH241 Calculus III, MATH240 and MATH246.

**UMD MATH141** (Calculus II) is the second course in the University of Maryland, College Park calculus sequence. It carries 4 credits and needs a C- or better in MATH140. This guide maps every topic in the official description to a lesson you can practice right now.

## What UMD MATH141 covers

The UMD Schedule of Classes describes MATH141 as a continuation of MATH140, including techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, and sequences and series. Like MATH140, it notes that graphing calculators, or computers with suitable software, will be needed.

That is a full **Calculus 2** course. The official description does not list parametric equations or polar coordinates, so if your section covers them, your instructor's syllabus is the place to check. The description also does not spell out a weekly schedule or textbook.

## MATH141 topic map

| MATH141 topic | Practice | Read |
| --- | --- | --- |
| Inverse functions | [Inverse function derivatives](/learn/calculus-1/derivative-rules/inverse-function-derivatives) | [Inverse function rule](/rules/inverse-function-rule) |
| Exponential and log functions | [Exponential and log derivatives](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Derivatives of exponential and log functions](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Substitution | [u-substitution refresher](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [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 substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Volumes | [Volumes by disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Work, arc length, moments | [Work](/learn/calculus-2/improper-integrals-and-applications/work) | [Center of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) |
| Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Convergence tests](/blog/convergence-tests) |
| Series | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Geometric series](/blog/geometric-series), [ratio test](/rules/ratio-test) |

## MATH141 in the UMD sequence

| Course | Credits | Prerequisite |
| --- | --- | --- |
| [MATH140 Calculus I](/courses/university-of-maryland-math-140) | 4 | C- in MATH115 or placement |
| MATH141 Calculus II | 4 | C- in MATH140 |
| [MATH241 Calculus III](/courses/university-of-maryland-math-241) | 4 | C- in MATH141 |

MATH141 is a gateway course: MATH240 (linear algebra), MATH246 (differential equations) and MATH241 all list a C- or better in MATH141 as the prerequisite.

## How MATH141 builds on MATH140

MATH141 assumes you can differentiate quickly and evaluate basic definite integrals with the Fundamental Theorem of Calculus. The course then asks harder questions: how to integrate products, powers of trig functions and rational functions, what an integral over an infinite interval means, and when an infinite sum adds up to a finite number. If your MATH140 skills are rusty, spend the first week on the [antiderivative practice](/learn/calculus-1/integrals/antiderivative-practice) and [u-substitution](/learn/calculus-1/integrals/u-substitution) lessons before new material piles up.

## Example problems at the MATH141 level

**1. Integration by parts.** With $u = x$ and $dv = e^x\,dx$:

$$\int x e^x\,dx = x e^x - \int e^x\,dx = x e^x - e^x + C$$

**2. An improper integral.**

$$\int_1^\infty \frac{1}{x^2}\,dx = \lim_{b \to \infty}\left[-\frac{1}{x}\right]_1^b = 0 - (-1) = 1$$

**3. A geometric series.** With first term $3$ and ratio $\frac{1}{2}$:

$$\sum_{n=0}^{\infty} 3\left(\frac{1}{2}\right)^n = \frac{3}{1 - \frac{1}{2}} = 6$$

## How to do well in MATH141

- **Practice choosing a method, not just executing it.** The [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) lesson mixes integrals so you have to decide which technique fits.
- **Draw every volume problem.** Sketch the region and one slice before writing an integral.
- **Make a series test flowchart** and check it against the [convergence tests guide](/blog/convergence-tests).
- **Review exponentials and logs early**, since they appear in almost every integration technique.
- **Use [practice problems on integration by parts](/practice-problems/integration-by-parts)** and timed [practice exams](/practice) before each test.

> **Tip:** before testing a series for convergence, check the $n$th term. If the terms do not go to $0$, the series diverges and you are done.

## Frequently asked questions

### What is MATH141 at UMD?

MATH141 Calculus II continues MATH140. The Schedule of Classes lists techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, and sequences and series.

### What is the prerequisite for MATH141?

A minimum grade of C- in MATH140.

### Is MATH141 harder than MATH140?

Many students find it harder, mostly because integration techniques and series tests need judgment about which method to use. Short, frequent practice sessions on choosing a strategy help a lot.

### Why are exponential and log functions in MATH141?

UMD names inverse, exponential and logarithmic functions in the MATH141 description rather than in MATH140. Expect to study their derivatives and integrals in this course.

### What comes after MATH141?

MATH241 Calculus III requires a minimum grade of C- in MATH141. MATH141 is also the prerequisite for MATH240 Introduction to Linear Algebra and MATH246 Differential Equations for Scientists and Engineers.