# IU MATH-M 212 Calculus II: Syllabus, Topics and Practice

> A study guide for Indiana University Bloomington MATH-M 212 Calculus II: integration techniques, improper integrals, volume, work and series.

Source: https://practicecalculus.com/courses/indiana-university-math-m212
Updated: 2026-11-08

## At a glance

- **Course code:** MATH-M 212
- **Credits:** 4
- **Prerequisites:** Not listed on the IU course page; it follows MATH-M 211 Calculus I
- **Covers:** Integration by parts, trigonometric substitutions, partial fractions, improper integrals, volume, work, arclength, surface area, infinite series
- **Honors version:** MATH-S 212 Honors Calculus II
- **Next course:** MATH-M 311 Calculus 3
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH-M 212 is the 4-credit Calculus II course at Indiana University Bloomington.
- It covers integration by parts, trigonometric substitutions, partial fractions, improper integrals, volume, work, arclength, surface area and infinite series.
- It follows MATH-M 211 and leads to MATH-M 311 Calculus 3.
- MATH-S 212 Honors Calculus II is the honors option.

**IU MATH-M 212** (Calculus II) is the second calculus course at Indiana University Bloomington, after MATH-M 211. It carries 4 credits and is offered by the College of Arts and Sciences. This guide maps each topic in the official description to lessons you can practice with instant feedback.

## What IU MATH-M 212 covers

IU's official course listing describes MATH-M 212 as: techniques of integration (by parts, trigonometric substitutions, partial fractions), improper integrals, volume, work, arclength, surface area, infinite series.

That is a standard **Calculus 2** course. The listing is a short summary, so it does not name a textbook, schedule or prerequisite, and it does not say whether power series, Taylor series, parametric curves or polar coordinates are included. Check your section syllabus for those details. An honors version, MATH-S 212 Honors Calculus II, is also offered.

## MATH-M 212 topic map

| M212 topic | Practice | Read |
| --- | --- | --- |
| Substitution review | [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) |
| Repeated parts | [Repeated parts and LIATE](/learn/calculus-2/integration-techniques/repeated-parts-and-liate) | [Integration by parts rule](/rules/integration-by-parts-rule) |
| Trigonometric substitutions | [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) |
| Volume | [Volumes by washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Work | [Work](/learn/calculus-2/improper-integrals-and-applications/work) | [Projections and work](/learn/calculus-3/vectors-and-space/projections-and-work) |
| Arclength and surface area | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Parametric arc length](/learn/calculus-2/power-series-parametric-polar/parametric-arc-length) |
| Infinite series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Convergence tests](/blog/convergence-tests) |
| Convergence tests | [Integral test and p-series](/learn/calculus-2/sequences-and-series/integral-test-and-p-series) | [Nth term test](/rules/nth-term-test), [ratio test](/rules/ratio-test) |

## M212 in the IU Bloomington sequence

| Course | Credits | Covers |
| --- | --- | --- |
| [MATH-M 211 Calculus I](/courses/indiana-university-math-m211) | 4 | Limits, derivatives, integrals, applications |
| MATH-M 212 Calculus II | 4 | Integration techniques, improper integrals, applications, series |
| [MATH-M 311 Calculus 3](/courses/indiana-university-math-m311) | 3 to 5 | Several variables, partial derivatives, multiple integrals |

## How M212 builds on M211

M212 assumes you can differentiate quickly and evaluate basic definite integrals with the Fundamental Theorem of Calculus from M211. The first part of the course adds new ways to find antiderivatives. The middle part uses integrals as a tool to measure volumes, lengths, surface areas and work. The last part changes direction and asks when an infinite sum adds up to a finite number, which needs careful use of limits. Students who keep their M211 skills sharp usually find the transition much smoother.

## Example problems at the M212 level

**1. A trig substitution.** With $x = \sin\theta$:

$$\int \frac{dx}{\sqrt{1 - x^2}} = \int d\theta = \arcsin x + C$$

**2. Work.** A spring with $k = 10$ N/m stretched from $0$ to $0.5$ m:

$$W = \int_0^{0.5} 10x\,dx = 5x^2\Big|_0^{0.5} = 1.25 \text{ J}$$

**3. A p-series.** $\sum_{n=1}^{\infty} \frac{1}{n^2}$ converges because $p = 2 > 1$, while $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ diverges because $p = \frac{1}{2} \le 1$.

## How to do well in MATH-M 212

- **Review M211 integrals first.** Every new technique ends with a basic antiderivative, so the [antiderivative practice](/learn/calculus-1/integrals/antiderivative-practice) lesson is a smart warm-up.
- **Practice choosing a technique** with mixed sets like [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy).
- **Set up applications from a slice.** For volume, work and arclength, write the formula for one thin piece first.
- **Give series extra time.** Work through [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) and [convergence tests problems](/practice-problems/convergence-tests).
- **Take timed [practice exams](/practice)** and use the IU Math Learning Center when you are stuck.

> **Tip:** an improper integral is a limit. Replace the infinite bound or the bad point with a variable, integrate, then take the limit.

## Frequently asked questions

### What is MATH-M 212 at Indiana University?

MATH-M 212 Calculus II is the second course in the IU Bloomington calculus sequence. IU lists techniques of integration (by parts, trigonometric substitutions, partial fractions), improper integrals, volume, work, arclength, surface area, and infinite series.

### How many credits is MATH-M 212?

IU lists MATH-M 212 at 4 credits.

### What do I need before MATH-M 212?

The IU course page does not print a prerequisite. M212 follows MATH-M 211 Calculus I, so plan on completing M211 or equivalent credit first and confirm with your advisor.

### Does M212 cover power series and Taylor series?

The official description says infinite series without listing power series or Taylor series by name. Your section syllabus will say how far the series unit goes.

### What comes after MATH-M 212?

MATH-M 311 Calculus 3, which covers the geometry of 2-, 3- and n-space, functions of several variables, partial differentiation, max and min problems, and multiple integration.