# ASU MAT 266 Calculus for Engineers II: Study Guide and Practice

> A study guide for ASU MAT 266 Calculus for Engineers II: methods of integration, applications, improper integrals and Taylor series, with practice.

Source: https://practicecalculus.com/courses/arizona-state-mat-266
Updated: 2026-11-03

## At a glance

- **Course code:** MAT 266
- **Credit hours:** 3
- **General studies:** Mathematical Studies (MATH / MA)
- **Covers:** Methods of integration, applications of calculus, elements of analytic geometry, improper integrals, Taylor series
- **Offered by:** School of Mathematical and Statistical Sciences
- **Next course:** MAT 267 Calculus for Engineers III
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MAT 266 Calculus for Engineers II is the second course in ASU's engineering calculus sequence, worth 3 credit hours.
- It covers methods of integration, applications of calculus, elements of analytic geometry, improper integrals and Taylor series.
- It follows MAT 265 and leads to MAT 267, the multivariable course.
- MAT 271 is the 4-credit counterpart in the Calculus with Analytic Geometry sequence.

**ASU MAT 266**, Calculus for Engineers II, is the second course in Arizona State University's engineering calculus sequence. It follows MAT 265 and finishes single-variable calculus with integration techniques, applications and Taylor series. This guide maps every MAT 266 topic to a lesson you can practice with instant feedback.

## What ASU MAT 266 covers

The ASU catalog lists methods of integration, applications of calculus, elements of analytic geometry, improper integrals and Taylor series. It is a 3-credit-hour course that counts toward Mathematical Studies.

That is a standard **Calculus 2**. "Elements of analytic geometry" typically means curves such as conics, and parametric and polar descriptions of curves. Taylor series are the main series topic named, so expect convergence ideas to appear in support of them. On PracticeCalculus, MAT 266 lines up with the Calculus 2 path.

The course splits naturally into two halves. The first is about integration: learning substitution, parts, trigonometric integrals and partial fractions, then applying integrals to areas, volumes, arc length and work, and extending them to improper integrals over infinite intervals. The second half turns to curves and approximation: describing curves with analytic geometry, then representing functions as Taylor series. Students who keep practicing the first half while learning the second tend to find the final exam far less stressful.

## MAT 266 topic map

| MAT 266 topic | Practice | Read |
| --- | --- | --- |
| 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 guide](/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) |
| Applications: area and volume | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Applications: arc length, work | [Work](/learn/calculus-2/improper-integrals-and-applications/work) | [Area between curves](/blog/area-between-curves) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Analytic geometry: parametric and polar | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Implicit differentiation](/blog/implicit-differentiation) |
| Series background | [Geometric series](/learn/calculus-2/sequences-and-series/geometric-series) | [Convergence tests](/blog/convergence-tests) |
| Taylor series | [Common Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-theorem) |

## MAT 266 among ASU's second-semester options

| Course | Credit hours | Catalog topics |
| --- | --- | --- |
| [MAT 265 Calculus for Engineers I](/courses/arizona-state-mat-265) | 3 | The course before MAT 266 |
| MAT 266 Calculus for Engineers II | 3 | Integration methods, applications, analytic geometry, improper integrals, Taylor series |
| MAT 271 Calculus with Analytic Geometry II | 4 | Integration methods, applications, analytic geometry, improper integrals, sequences and series |
| [MAT 267 Calculus for Engineers III](/courses/arizona-state-mat-267) | 3 | The course after MAT 266 |

## Example problems at the MAT 266 level

**1. An improper integral.**

$$\int_0^{\infty} e^{-2x}\,dx = \lim_{t \to \infty}\left[-\frac{1}{2}e^{-2x}\right]_0^t = \lim_{t \to \infty}\left(\frac{1}{2} - \frac{1}{2}e^{-2t}\right) = \frac{1}{2}$$

**2. Partial fractions.** Since $\frac{1}{x(x + 1)} = \frac{1}{x} - \frac{1}{x + 1}$,

$$\int \frac{dx}{x(x + 1)} = \ln|x| - \ln|x + 1| + C$$

**3. A Maclaurin series.** The derivatives of $\sin x$ at $0$ cycle through $0, 1, 0, -1$, so

$$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots = x - \frac{x^3}{6} + \frac{x^5}{120} - \cdots$$

## How to do well in MAT 266

- **Practice choosing the technique.** The [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) lesson mixes methods the way exams do.
- **Learn LIATE for parts.** Picking $u$ well is most of the battle. See [repeated parts and LIATE](/learn/calculus-2/integration-techniques/repeated-parts-and-liate).
- **Memorize five Maclaurin series**: $e^x$, $\sin x$, $\cos x$, $\ln(1 + x)$ and $\frac{1}{1-x}$. New series are usually built from these.
- **Keep the [formula sheet](/formulas) open** for trig identities, review [common calculus mistakes](/blog/common-calculus-mistakes), and use timed [practice exams](/practice).

> **Tip:** an improper integral is just a limit of ordinary integrals. Write the limit explicitly every time and the convergence question answers itself.

## Frequently asked questions

### What is ASU MAT 266?

MAT 266 Calculus for Engineers II is a 3-credit-hour course at ASU. The catalog lists methods of integration, applications of calculus, elements of analytic geometry, improper integrals and Taylor series.

### What is the difference between MAT 266 and MAT 271?

Both are second-semester calculus courses. MAT 266 is the 3-credit engineering version, while MAT 271 Calculus with Analytic Geometry II is 4 credits and its catalog description names sequences and series in general rather than only Taylor series.

### What comes after MAT 266?

MAT 267 Calculus for Engineers III, which covers vector-valued functions of several variables, partial derivatives and multiple integration.

### Is MAT 266 hard?

Calculus 2 is often seen as the hardest course in a calculus sequence, because you must choose an integration method rather than follow one rule. Mixed practice that makes you pick the technique is the best preparation.

### What should I review before MAT 266?

Antiderivatives, u-substitution and the Fundamental Theorem of Calculus from MAT 265, plus trig identities for trigonometric integrals.