UBC MATH 101 Integral Calculus: Topics, Study Guide and Practice

MATH 101 is UBC Vancouver's second-term calculus course, titled Integral Calculus with Applications. It follows MATH 100 or another first differential calculus course, and it takes students from the definite integral through integration techniques to infinite series. This guide maps every MATH 101 topic to practice, so you can build integration skills one problem at a time.

What UBC MATH 101 covers

The UBC Vancouver calendar summarizes MATH 101 as the definite integral, integration techniques, applications, modelling and infinite series. It is worth 3 credits with three lecture hours per week, and it is listed as equivalent to MATH 103 and MATH 105.

In a standard sequence, that is the integral half of Calculus 1 plus the core of Calculus 2. The calendar does not list individual techniques or tests, so the map below covers the topics a typical integral calculus course includes under those headings: substitution and integration by parts, applications such as area and volume, and convergence of series.

MATH 101 topic map

MATH 101 and its equivalents

After MATH 101, students continue to MATH 200, Calculus III, or another multivariable course such as MATH 253.

Example problems at the MATH 101 level

1. A substitution. Evaluate \int_0^1 2x(x^2 + 1)^3\,dx with u = x^2 + 1, du = 2x\,dx:

2. Partial fractions. Since \dfrac{1}{x^2 - 1} = \dfrac{1}{2}\left(\dfrac{1}{x - 1} - \dfrac{1}{x + 1}\right),

3. A geometric series.

How to do well in UBC MATH 101

• Practice choosing a technique. The hardest part of integration is deciding what to try. The choosing a strategy lesson trains exactly that.
• Build series intuition early. Start with the geometric series formula, then learn each test in the convergence tests guide.
• Keep a formula sheet nearby. The calculus formula sheet lists common integrals and series.
• Simulate exams. Mixed, timed sets in practice and the plan in how to prepare for a calculus exam get you ready for midterms and the final.

Tip: draw the region before every area or volume problem. A ten-second sketch tells you which curve is on top and where the limits of integration are.