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

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 vs MATH 1172

You can only take one of the two. For the first course in the sequence, see the MATH 1151 guide. The MATH 1172 guide covers the engineering track, and the MATH 2153 guide 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:

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

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

How to do well in Ohio State MATH 1152

• Learn integration as a decision. Practice 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 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, and keep the formula sheet for Maclaurin series.
• Review 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.