UW MATH 125: Calculus with Analytic Geometry II

MATH 125 covers integral calculus: techniques of integration, applications like volume and work, and an introduction to differential equations. It's the second quarter of UW's calculus sequence and a prerequisite for most engineering and physical science coursework.

Fennie is independent and not affiliated with University of Washington. This is an unofficial study guide.

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What makes it hard

Integration technique selection is the core challenge — knowing whether a problem wants substitution, parts, partial fractions, or a trig identity, under exam time pressure. The applications (work, center of mass) demand careful setup, and many students find 125 harder than 124 because there's less to fall back on from high school.

What you'll cover

• Definite and indefinite integrals
• Substitution and integration by parts
• Trigonometric integrals and partial fractions
• Areas, volumes, and work
• Improper integrals
• Intro to differential equations

The MATH 125 study guide

How to study for UW MATH 125, step by step.

1
Get derivatives and trig identities cold before week two
Integration is differentiation run backward, and most MATH 125 mistakes are really algebra or trig mistakes. A few days of focused review up front pays off all quarter.
2
Mix integration techniques every day
Don't practice substitution Monday and parts Tuesday — shuffle them. Exams hand you a bare integral and the real skill is recognizing which technique applies, which only interleaved practice builds.
3
Set up application problems without solving them
Volumes, work, and center of mass live or die on the setup integral. Practice writing the integral from the physical description, check it against the solution, and only then grind the computation.
4
Run the past final archive under exam timing
The math department's posted MATH 125 finals are harder than the homework and calibrated to the real thing. Make timed archive runs a weekly habit in the second half of the quarter.
5
Hand the drill schedule to Fennie
Upload the MATH 125 syllabus and Fennie's Daily Plan mixes techniques daily and paces everything to your exam dates, generating practice quizzes from your actual course materials. Free to start.
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How Fennie helps with MATH 125

Daily Plans turn MATH 125 into a steady drill schedule, mixing integration techniques daily so you build the pattern recognition exams demand. Chat through why a particular technique applies, and use practice quizzes to simulate the technique-selection pressure of the real exam.

FAQ

Is MATH 125 harder than MATH 124?

Many UW students say yes — integration is less formulaic than differentiation, and the applications require careful setup. The exam style is just as word-problem heavy.

What should I review before MATH 125?

Derivatives cold, trig identities, and algebraic manipulation. Most integration mistakes are actually algebra or trig mistakes.

How many hours a week does MATH 125 take?

Plan on 10–15 hours outside lecture. Five-credit quarter-system calculus moves through a semester's worth of integration in ten weeks.

Pass MATH 125 with a plan, not a cram

Upload your MATH 125 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.

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More UW courses

MATH 124 — Calculus with Analytic Geometry I

MATH 124 is UW's first-quarter calculus course: limits, derivatives, and their applications, taught with an emphasis on word problems and graphical reasoning. It's required for engineering, CS, and most science majors, making it one of the largest courses on campus.

MATH 126 — Calculus with Analytic Geometry III

MATH 126 finishes UW's calculus sequence with multivariable calculus — vectors, partial derivatives, double integrals — plus Taylor polynomials and Taylor series taught from UW's own course notes. It's the final calculus prerequisite for most STEM majors.

MATH 207 — Introduction to Differential Equations

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MATH 208 — Matrix Algebra with Applications

MATH 208 (formerly MATH 308) is UW's applied linear algebra course: systems of linear equations, matrices, vector spaces, subspaces, orthogonality, least squares, eigenvalues, and eigenvectors. As of autumn 2021, either the 208 or 308 number counts toward degree requirements. It underpins machine learning, graphics, and most quantitative fields.