UW MATH 125 Calculus II: Topics, Study Guide and Practice
A study guide for University of Washington MATH 125 (Calculus with Analytic Geometry II): integrals, techniques and applications, with free practice.
University of Washington Updated 3 min read
At a glance
- Course code
- MATH 125
- Credits
- 5 (one quarter)
- Offered
- Autumn, winter, spring and summer
- Prerequisites
- Minimum grade of 2.0 in MATH 124, or a score of 3 on the AP Calculus AB or BC exam
- Covers
- Second quarter of single-variable calculus, emphasizing integral calculus, applications and problem solving
- Next course
- MATH 126 (Calculus with Analytic Geometry III)
- Practice here
- Calculus 1 integrals and Calculus 2
On this page
UW MATH 125, Calculus with Analytic Geometry II, is the second quarter of calculus at the University of Washington. It is a 5-credit course offered every quarter, and it is all about the integral. This guide maps the MATH 125 material to practice with instant feedback.
What UW MATH 125 covers
The UW course catalog describes MATH 125 as the second quarter of single-variable calculus. It emphasizes integral calculus, along with applications and problem solving. You need a minimum grade of 2.0 in MATH 124, or a 3 on the AP Calculus AB or BC exam. It cannot be taken for credit if you already have credit for MATH 207.
The catalog does not list subtopics. A course on integral calculus at this point in a sequence typically covers what is split between the end of Calculus 1 and the start of Calculus 2 elsewhere: antiderivatives, the definite integral, the Fundamental Theorem, substitution, applications such as area and volume, and integration techniques. Check your section's syllabus for the exact list. Series and Taylor polynomials appear in MATH 126 at UW.
MATH 125 topic map
| Integral calculus topic | Practice | Read |
|---|---|---|
| Antiderivatives | Undoing derivatives | Antiderivatives, reverse power rule |
| Riemann sums | Area with rectangles | Riemann sums |
| The definite integral | The definite integral as area | Definite integral properties |
| Fundamental Theorem of Calculus | Derivatives of integrals | Fundamental Theorem of Calculus |
| Substitution | U-substitution | U-substitution |
| Net change and average value | Average value | Mean value theorem for integrals |
| Area between curves | Area between curves | Area between curves |
| Volumes | Volumes with disks | Volumes of revolution |
| Work and physical applications | Work | Center of mass |
| Integration by parts | Integration by parts | Integration by parts |
| Trig integrals and substitution | Trig substitution | Trig substitution |
| Partial fractions | Partial fractions | Partial fractions |
| Improper integrals | Integrating to infinity | Improper integrals |
| Differential equations | Separable differential equations | Antiderivatives |
MATH 125 in the UW sequence
| Course | Credits | Prerequisite | Emphasis |
|---|---|---|---|
| MATH 124 | 5 | Guided Self-Placement recommended | Differential calculus |
| MATH 125 | 5 | 2.0 in MATH 124, or AP AB or BC score of 3 | Integral calculus |
| MATH 126 | 5 | 2.0 in MATH 125 or 135, or AP BC score of 4 | Vectors, multivariable derivatives, Taylor series |
The honors alternative is MATH 135, the second quarter of the accelerated sequence. See the MATH 124 guide for the first quarter and the MATH 126 guide for what comes next.
Example problems at the MATH 125 level
1. FTC part 2. Evaluate \int_0^{\pi} \sin x\,dx:
2. Area between curves. The curves y = x and y = x^2 meet at x = 0 and x = 1, with x \ge x^2 between them:
3. Substitution. With u = \ln x, du = \frac{dx}{x}:
How to do well in UW MATH 125
- Make the derivative rules automatic first. Every integral check is a derivative. Revisit derivative rules practice if they feel slow.
- Practice choosing a method. Once you know several techniques, work choosing a strategy problems where the method is not given.
- Draw every application. Area and volume setups come from the picture. The volumes of revolution guide shows how.
- Use the formula sheet for common integrals, and take timed practice exams. Review common calculus mistakes before each exam.
Tip: check any antiderivative by differentiating it. If you get back the integrand, it is right.
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Undoing derivatives
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