# UF MAC 2312 Calculus 2: Topics, Study Guide and Practice

> A study guide for UF MAC 2312 Analytic Geometry and Calculus 2: integration techniques, applications, inverse trig functions and series, with practice.

Source: https://practicecalculus.com/courses/university-of-florida-mac-2312
Updated: 2026-11-03

## At a glance

- **Course code:** MAC 2312
- **Credits:** 4
- **Prerequisites:** MAC 2311 or MAC 3472 with a minimum grade of C
- **Covers:** Techniques of integration, applications of integration, differentiation and integration of inverse trig, exponential and log functions, sequences and series
- **Honors version:** MAC 3473 Honors Calculus 2
- **Next course:** MAC 2313 Analytic Geometry and Calculus 3
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MAC 2312 is Calculus 2 at the University of Florida, a 4-credit General Education mathematics course.
- It covers integration techniques and applications, calculus of inverse trig, exponential and log functions, and sequences and series.
- It requires a C or better in MAC 2311 or MAC 3472.
- Credit is given for at most one of MAC 2312, MAC 2512 and MAC 3473.

**UF MAC 2312** (Analytic Geometry and Calculus 2) is the second course in the University of Florida calculus sequence. Students arrive from MAC 2311 or the honors MAC 3472, and the course finishes single-variable calculus before multivariable work in MAC 2313. This guide maps each MAC 2312 topic to a lesson you can practice with instant feedback.

## What UF MAC 2312 covers

The UF catalog lists four topics: techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential and logarithmic functions; and sequences and series.

That is a standard **Calculus 2**. The inverse trig, exponential and log material revisits functions from Calculus 1 with a focus on their integrals, such as $\int \frac{dx}{1 + x^2} = \arctan x + C$. The rest lines up with the integration techniques, applications, and sequences and series units on PracticeCalculus. Power series and Taylor series usually fall under the series topic.

## MAC 2312 topic map

| MAC 2312 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 guide](/blog/integration-by-parts) |
| Trig integrals | [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) |
| Inverse trig functions | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Arcsine](/functions/arcsine), [arctangent](/functions/arctangent) |
| Exponential and log functions | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Natural logarithm](/functions/natural-logarithm), [logarithmic differentiation](/rules/logarithmic-differentiation) |
| Applications of integration | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [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) | [Limits at infinity](/blog/limits-at-infinity) |
| Series and convergence tests | [Integral test and p-series](/learn/calculus-2/sequences-and-series/integral-test-and-p-series) | [Convergence tests](/blog/convergence-tests) |
| Power and Taylor series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series), [Taylor series](/blog/taylor-series) |

## MAC 2312 in the UF sequence

| Course | Credits | Prerequisite (from the catalog) |
| --- | --- | --- |
| [MAC 2311 Calculus 1](/courses/university-of-florida-mac-2311) | 4 | Placement exam, or C in MAC 1147 or higher |
| MAC 2312 Calculus 2 | 4 | MAC 2311 or MAC 3472 with a C |
| [MAC 2313 Calculus 3](/courses/university-of-florida-mac-2313) | 4 | MAC 2312, MAC 2512 or MAC 3473 with a C |

The honors equivalent is MAC 3473 Honors Calculus 2, which continues the honors sequence. You can receive credit for only one of MAC 2312, MAC 2512 and MAC 3473.

## Example problems at the MAC 2312 level

**1. A trig integral.** Using $\sin^2 x = \frac{1 - \cos 2x}{2}$:

$$\int \sin^2 x\,dx = \frac{x}{2} - \frac{\sin 2x}{4} + C$$

**2. An inverse trig integral.**

$$\int_0^{1/2} \frac{dx}{\sqrt{1 - x^2}} = \arcsin\frac{1}{2} - \arcsin 0 = \frac{\pi}{6}$$

**3. A comparison test.** $\sum_{n=1}^{\infty} \frac{1}{n^2 + 1}$ converges, because $0 < \frac{1}{n^2 + 1} < \frac{1}{n^2}$ and $\sum \frac{1}{n^2}$ is a convergent p-series with $p = 2$.

## How to do well in MAC 2312

- **Build a method checklist.** Try substitution, then parts, trig identities, trig substitution and partial fractions. The [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) lesson trains that decision.
- **Memorize the inverse trig integrals.** $\arcsin$ and $\arctan$ show up constantly. Put them on your own summary next to the [formula sheet](/formulas).
- **Anchor series on known families:** the [geometric series formula](/rules/geometric-series-formula) and p-series. Most comparison problems use one of them.
- **Study the classic slips** in [common calculus mistakes](/blog/common-calculus-mistakes), and take timed [practice exams](/practice) before each exam.

> **Tip:** you need a C in MAC 2312 to move on to MAC 2313. Keep a running list of problems you missed and redo them the week before each exam.

## Frequently asked questions

### What is MAC 2312 at UF?

MAC 2312 Analytic Geometry and Calculus 2 is UF's second-semester calculus course. The catalog lists techniques of integration, applications of integration, differentiation and integration of inverse trigonometric, exponential and logarithmic functions, and sequences and series.

### What do I need to take MAC 2312?

MAC 2311 or MAC 3472 with a minimum grade of C.

### What comes after MAC 2312?

MAC 2313 Analytic Geometry and Calculus 3, which covers solid analytic geometry, vectors, partial derivatives and multiple integrals. It requires MAC 2312, MAC 2512 or MAC 3473 with a C.

### Is MAC 2312 harder than MAC 2311?

Many students find Calculus 2 the hardest course in the sequence. Integration techniques and series tests require choosing a method from several options, which takes more practice than applying a single rule.

### How do I study for MAC 2312 exams?

Work mixed problem sets where the technique is not given, keep a short list of which clues point to which method, and review convergence tests with a fixed order of attack.