# TAMU MATH 152 Engineering Math II: Topics, Study Guide, Practice

> A study guide for Texas A&M MATH 152 (Engineering Mathematics II): integration techniques, applications, improper integrals and series, with practice.

Source: https://practicecalculus.com/courses/texas-am-math-152
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 152 (Texas common course number MATH 2414)
- **Credits:** 4 (3 lecture hours, 2 lab hours)
- **Prerequisites:** C or better in MATH 151 or equivalent, plus C or better in MATH 150 or equivalent or an acceptable placement score
- **Covers:** Integration techniques, area, volume and work, improper integrals, approximate integration, vectors, infinite, power and Taylor series
- **Harder version:** MATH 172 (Calculus II)
- **Next course:** MATH 251 (Engineering Mathematics III)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 152 is the second semester of the Texas A&M engineering calculus sequence, worth 4 credits with a lab.
- Its two big themes are integration (techniques and applications such as area, volume and work) and infinite series through Taylor series.
- It needs a C or better in MATH 151 and leads to MATH 251, multivariable calculus.
- MATH 172 is the more demanding version, and only one of MATH 148, 152 or 172 counts toward a degree.

**Texas A&M MATH 152**, Engineering Mathematics II, is the second calculus course for Aggie engineers and science majors. It takes the derivatives and basic integrals from MATH 151 and turns them into a full toolkit: integration techniques, physical applications, and infinite series. This page maps each MATH 152 topic to practice problems with instant feedback.

## What Texas A&M MATH 152 covers

The catalog description lists differentiation and integration techniques with applications to area, volume and work, then improper integrals and approximate (numerical) integration. The course also includes analytic geometry and vectors, and it finishes with infinite series, power series and Taylor series, with a computer algebra component throughout.

That matches a standard **Calculus 2** course closely. Most of the semester is integration and series, which are exactly the four units of our Calculus 2 path.

## MATH 152 topic map

| MATH 152 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) |
| Trig integrals and trig 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) |
| Area and volume | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution), [area between curves](/blog/area-between-curves) |
| Work | [Work](/learn/calculus-2/improper-integrals-and-applications/work) | [Definite integral properties](/rules/definite-integral-properties) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Approximate integration | [Area with rectangles](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| Vectors | [The dot product](/learn/calculus-3/vectors-and-space/dot-product) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Infinite series | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Power and Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Power series](/blog/power-series), [Taylor series](/blog/taylor-series) |

## MATH 152 in the Texas A&M sequence

| Course | Title | Credits | Role |
| --- | --- | --- | --- |
| MATH 151 | Engineering Mathematics I | 4 | Prerequisite: limits, derivatives, first integrals |
| MATH 152 | Engineering Mathematics II | 4 | Integration and series |
| MATH 172 | Calculus II | 4 | More demanding alternative to MATH 152 |
| MATH 251 | Engineering Mathematics III | 3 | Next: multivariable calculus |

If MATH 151 feels shaky, revisit it with the [MATH 151 guide](/courses/texas-am-math-151) first. When you finish MATH 152, the [MATH 251 guide](/courses/texas-am-math-251) shows what comes next.

## Example problems at the MATH 152 level

**1. Integration by parts.** Evaluate $\int x\cos x\,dx$. Let $u = x$ and $dv = \cos x\,dx$, so $du = dx$ and $v = \sin x$:

$$\int x\cos x\,dx = x\sin x - \int \sin x\,dx = x\sin x + \cos x + C$$

**2. Work.** A force $F(x) = 6x$ newtons moves an object from $x = 0$ to $x = 2$ meters. The work is

$$W = \int_0^2 6x\,dx = \left[3x^2\right]_0^2 = 12 \text{ J}$$

**3. A geometric series.** Find the sum of $\sum_{n=0}^{\infty} 5\left(\frac{1}{3}\right)^n$. The ratio is $r = \frac{1}{3}$, so $|r| < 1$ and

$$\sum_{n=0}^{\infty} 5\left(\tfrac{1}{3}\right)^n = \frac{5}{1 - \frac{1}{3}} = \frac{15}{2}$$

## How to do well in MATH 152

- **Practice choosing the method, not just applying it.** Exams mix techniques, so work through [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) once you know each one.
- **Learn LIATE for parts.** The [integration by parts rule](/rules/integration-by-parts-rule) is fast once picking $u$ is a habit.
- **Build series intuition from geometric series.** The [geometric series formula](/rules/geometric-series-formula) and the [nth-term test](/rules/nth-term-test) settle many problems before you need a heavier test.
- **Keep the [formula sheet](/formulas) open** for trig identities and common integrals, and time yourself on [practice exams](/practice).
- **Review the classic errors** in [common calculus mistakes](/blog/common-calculus-mistakes), especially forgotten constants and dropped negative signs.

> **Tip:** for every improper integral, write the limit explicitly before integrating. It prevents the most common lost points.

## Frequently asked questions

### What is MATH 152 at Texas A&M?

MATH 152, Engineering Mathematics II, is the Calculus 2 course for engineering and science majors. It covers integration techniques and applications, improper integrals, approximate integration, vectors and infinite series including power and Taylor series.

### What do I need before MATH 152?

The catalog requires a C or better in MATH 151 or an equivalent course, together with a C or better in MATH 150 or equivalent, or an acceptable math placement score.

### Is MATH 152 harder than MATH 151?

Many students find it harder, because integration techniques require choosing a method rather than following one rule, and series are a new way of thinking. Regular practice with mixed problems makes the biggest difference.

### What is the difference between MATH 152 and MATH 172?

MATH 172 (Calculus II) is described as more demanding than MATH 152. It covers integration techniques, applications, improper integrals, sequences, series and solid analytic geometry.

### What comes after MATH 152?

MATH 251, Engineering Mathematics III, which covers vector algebra, functions of several variables, multiple integrals, and line and surface integrals.