# Ohio State MATH 1152 Calculus II: Topics, Study Guide, Practice

> A study guide for Ohio State MATH 1152 (Calculus II): integration techniques, sequences and series, parametric curves and polar coordinates, with practice.

Source: https://practicecalculus.com/courses/ohio-state-math-1152
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1152
- **Credit hours:** 5
- **Offered:** Autumn, spring and summer
- **Prerequisites:** C- or above in MATH 1114 (114), 1151, 1156, 1161.xx, 152.xx, 161.xx or 161.01H
- **Covers:** Integral calculus, sequences and series, parametric curves, polar coordinates, with vectors as an optional topic
- **Next course:** MATH 2153 (Calculus III)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 1152 is Ohio State's 5-credit Calculus II course, offered in autumn, spring and summer.
- It covers integral calculus, sequences and series, parametric curves and polar coordinates, with vectors listed as optional.
- It is not open to students with credit for MATH 1172, the engineering alternative.
- It leads to MATH 2153, Calculus III.

**Ohio State MATH 1152**, Calculus II, is the second semester of Ohio State's main calculus sequence. It is a 5-credit course covering integral calculus, sequences and series, parametric curves and polar coordinates. This guide maps each MATH 1152 topic to practice problems with instant feedback, so you can learn by doing.

## What Ohio State MATH 1152 covers

The catalog description lists integral calculus, sequences and series, parametric curves and polar coordinates, with vectors marked optional. The department's course description document fills in the details. It starts with integration strategies and applications: regions between curves, volume by slicing and by shells, arc length, surface area and physical applications. Integration by parts, trig integrals, trig substitution, partial fractions and improper integrals follow.

The second half moves to sequences and series with the divergence, integral, ratio, root, comparison and alternating series tests, then power series and Taylor series. The topic list also includes a short unit on differential equations (direction fields, Euler's method and separable equations), followed by parametric and polar equations and an introduction to vectors.

This is a full **Calculus 2** course, with a small preview of vectors from Calculus 3.

## MATH 1152 topic map

| MATH 1152 topic | Practice | Read |
| --- | --- | --- |
| Regions between curves | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves](/blog/area-between-curves) |
| Volume by slicing and shells | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Arc length, surface area, physical applications | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Work](/learn/calculus-2/improper-integrals-and-applications/work) |
| 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 | [Repeated factors](/learn/calculus-2/integration-techniques/partial-fractions-repeated) | [Partial fractions](/blog/partial-fractions) |
| Improper integrals | [Integrating to infinity](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Sequences and series | [Sequences and their limits](/learn/calculus-2/sequences-and-series/sequences) | [Geometric series](/blog/geometric-series) |
| Divergence and integral tests | [The integral test and p-series](/learn/calculus-2/sequences-and-series/integral-test-and-p-series) | [nth-term test](/rules/nth-term-test), [convergence tests](/blog/convergence-tests) |
| Ratio, root and comparison tests | [Ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Ratio test](/rules/ratio-test) |
| Alternating series | [Alternating series](/learn/calculus-2/sequences-and-series/alternating-series) | [Alternating series test](/rules/alternating-series-test) |
| Power and Taylor series | [Common Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Power series](/blog/power-series), [Taylor series](/blog/taylor-series) |
| Separable differential equations | [Separable differential equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Antiderivatives](/blog/antiderivatives) |
| Parametric and polar | [Area in polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-area) | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) |
| Vectors (optional) | [The dot product](/learn/calculus-3/vectors-and-space/dot-product) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |

## MATH 1152 vs MATH 1172

| | MATH 1152 | MATH 1172 |
| --- | --- | --- |
| Title | Calculus II | Engineering Mathematics A |
| Credit hours | 5 | 5 |
| Shared core | Integration techniques, Taylor series | Integration techniques, Taylor series |
| Distinctive topics | Full series tests, differential equations, polar | Several-variable differential calculus |
| Next course | MATH 2153 | MATH 2153 |

You can only take one of the two. For the first course in the sequence, see the [MATH 1151 guide](/courses/ohio-state-math-1151). The [MATH 1172 guide](/courses/ohio-state-math-1172) covers the engineering track, and the [MATH 2153 guide](/courses/ohio-state-math-2153) shows what comes next.

## Example problems at the MATH 1152 level

**1. Trig substitution.** Evaluate $\int \frac{dx}{\sqrt{1 - x^2}}$ with $x = \sin\theta$, $dx = \cos\theta\,d\theta$:

$$\int \frac{\cos\theta}{\cos\theta}\,d\theta = \theta + C = \arcsin x + C$$

**2. The ratio test.** Test $\sum_{n=1}^{\infty} \frac{n}{2^n}$:

$$\lim_{n \to \infty} \frac{n + 1}{2^{n+1}} \cdot \frac{2^n}{n} = \lim_{n \to \infty} \frac{n + 1}{2n} = \frac{1}{2} < 1$$

so the series converges.

**3. A separable equation.** Solve $\frac{dy}{dx} = xy$ with $y(0) = 2$. Separate: $\frac{dy}{y} = x\,dx$, so $\ln|y| = \frac{x^2}{2} + C$ and

$$y = 2e^{x^2/2}$$

## How to do well in Ohio State MATH 1152

- **Learn integration as a decision.** Practice [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) with mixed problems, since exams do not tell you which technique to use.
- **Make a series flowchart.** Know which test to try first. The [choosing a test lesson](/learn/calculus-2/sequences-and-series/choosing-a-test) walks through the order.
- **Work by hand.** The course page states that calculators are not permitted during exams, so practice arithmetic and algebra without one.
- **Use the sample exams** posted on the course page alongside timed [practice exams](/practice), and keep the [formula sheet](/formulas) for Maclaurin series.
- **Review** [common calculus mistakes](/blog/common-calculus-mistakes) before every midterm.

> **Tip:** when a series looks like a rational function of $n$, compare it to a p-series with the same leading powers. That one idea handles a large share of exam problems.

## Frequently asked questions

### What is MATH 1152 at Ohio State?

MATH 1152, Calculus II, is Ohio State's second calculus course. It covers integration techniques and applications, sequences and series, parametric curves and polar coordinates, with vectors as an optional topic.

### What do I need to take MATH 1152?

A C- or above in MATH 1151, 1156, 1161.xx, 1114 (114), 152.xx, 161.xx or 161.01H. It is not open to students with credit for 1172, 1181H or any math class numbered 1500 or above.

### What is the difference between MATH 1152 and MATH 1172?

MATH 1172, Engineering Mathematics A, covers integration techniques and Taylor series but replaces some series and polar material with an introduction to differential calculus of several variables. It is not open to math or actuarial science majors. Students can take only one of the two.

### Is MATH 1152 hard?

Many students find Calculus II the hardest of the sequence, because integration needs strategy and series require new reasoning. Mixed practice and the sample exams on the course page help a lot.

### What comes after MATH 1152?

MATH 2153, Calculus III, which covers multivariable differential and integral calculus.