basic integration

Math 141: Tutorial, Quiz Prep & WebWork #1

McGill Math 141, Cal 2, this is your week to get things moving! Three sessions to help you recover from the busyness of the start of term, get ready for that first quiz, take care of that first webwork and keep up with the material so far! & it’ll be e-z! Full details and registration on the Math 141 page.

Weekly Tutorial #2: Definite Integrals & the FTC

Friday Jan. 23rd, 5:30-7:30pm (M3-37A; $35/$40/$50*): this will be the second of 12 weekly tutorials covering all the theory and concepts from Math 141. We’ll be focusing on evaluating definite integrals and their relationship to FTC, as well as developing you intuitive understanding of the FTC. Detailed notes with fully developed solutions to highly representative practice problems included. *Registration and full details about pricing options on the Math 141 page.

Quiz #1 Prep Session

Saturday Jan. 24th, 1:00-3:00pm (M3-37A; $20/$15*): this 2h session will whip through the concepts and theory covered by the first quiz and focus on solving a number of highly representative problems based on quizzes from the previous years (drawing on a bank of >10 years). Acing quizzes right from the start is an easy way to take off some of the pressure on the final exam. Space is limited. *$20 for non-weekly members; $15 for fully-paid weekly members. Register on the Math 141 page.

WebWork #1 Workshop: No More Tears

Sunday Jan. 25th, 1-3pm (M3-37A; $20/$15*): a 2h session that will whip through problems that are structurally identical to your webwork problems, explaining the theory along the way. You won’t need Wolfram or Yahoo to answer your questions after this session. Save yourself the hours of banging your head against the wall & scouring the internet and get your assignment done quickly (while actually understanding it!). *$20 for non-weekly members; $15 for fully-paid weekly members. Register on the Math 141 page.

Mastery Sessions Registration

They’re here! Mastery Sessions for McGill Math 139 final exam prep; McGill Math 140 final exam prep and McGill Math 141 final exam prep. Everything you need to understand and succeed on your final. Space is limited and sessions usually fill up within ~72h of registration opening. Full details and registration at the links provided. Details for Math 263, 222 and 262 coming soon. Best of luck with the end of term!

MATH 141 – Integration Session & Final Review

Integration Session: Sunday April 6th 3-5pm, M3-37A on the third floor of McLennan. We’ll be covering 30-50 integrals from past exams. Students will have 30-60s to identify the correct method of integration and any other relevant information, then we’ll discuss the solution briefly as a group. $5-7 for Mastery Students; $20 for others. Please RSVP with Adaam at McGill.Calc.Help -at-; space is limited. Interested students should be proficient with the basics of each method of integration.

Final Review Session: Tuesday April 8th, 6-9pm, M3-17B on the third floor of McLennan. This will be a mock-final based on the sample final provided by Hundemer. In the fall term, his sample 140 final matched the actual exam very closely both in format and difficulty. As such, I’ll be writing a new exam similar to the sample in those respects, but with different questions. Students will have short intervals for attempting the problems followed by a brief discussion of the solution, as a group. $40, $10 off if you bring a friend. Please RSVP with Adaam at McGill.Calc.Help -at- See full details at the MATH 141 page.

Good luck with finals!

MATH 141 – Crash Course

Panicked about cal 2? Haven’t really started to review yet? No worries – we’ve got you covered :D. We’ll be running a crash-course for MATH 141 starting next Wednesday, April 9th, 2014. The aim of the crash will be to teach you the basics of everything you need to succeed and help you focus your studying most efficiently. The schedule:

  • Wednesday April 9th, 7:30-10:30pm – Methods of Integration: learn to integrate any expression. This session includes >100 examples from past exams as well as a complete summary and accessible explanation of each method of integration.
  • Thursday April 10th, 7:30-10:30pm – Applications of Integration: areas, volumes, arc-lengths, surface areas, FTC I&II, MVT. Learn to relate all these subjects to each other and reduce the load on your memory – includes simple explanations that will make the material intuitive and accessible.
  • Friday April 11th, 7:30-10:30pm – Polar & Parametric Everything: this session will cover everything from basic derivatives and tangent lines to curve-sketching, areas, lengths, surface area & more. We’ll look at tons of questions from past exams and consider strategies for dealing with these questions.
  • Saturday April 12th, 3:30-6:30pm – Sequences and Series: discover the easy way to understand sequences and series. We’ll review the tests for convergence and divergence and explain the logic behind them so that you can develop strong intuition about the behaviour of series. You’ll learn to assess the convergence /divergence of most exam-level series at a glance, as well as how to structure a formal solution.

This a small group crash course, which guarantees optimal interaction with the teacher. Sessions are $80/each or all 4 for $210, including detailed notes and tons of practice problems. For more information or to register, contact us at -at-

MATH 141 – Mastery Sessions

The second MATH 141 Mastery Session in preparation for the final exam will be tomorrow, Saturday March 29th from 12:30pm-3:30pm. Mastery 2 – Pre-session Worksheet Be sure to work through the questions and do a quick review of these topics so that you’re familiar with their basic application. As usual, the focus of the session will not be on understanding the ideas at an introductory level; rather, we’ll spend most of our time solving advanced exam-level questions and developing strategies for doing so. See you there!

MATH 141 – Integration Session

No theory. No algebra. No baby questions. As a follow-up to the first Mastery Session for MATH 141 this past Saturday, we’ll be running a session on exam-level integrals this coming Thursday from 6-8pm. Students will be given 30-60s to identify the correct method and setup the integral in an effort to help them develop this most important skill for Hundemer’s exam. We’ll be providing a list of ~30 classic integrals that you should definitely know, as well as an additional ~80 questions taken directly from the past 15 years of MATH 141 exams. The cost will be $5-10/h for students attending the mastery sessions; $15/h for non-mastery students (who can save $5 for every friend they bring); $40 at the door. RSVP by contacting Adaam at

MATH 141 – Special Promotion

For a limited time, if you recommend 5 people to the Mastery Sessions for MATH 141, you can attend all 5 sessions for only $25! Partial completion will also be eligible for a discount. We have posters and flyers available to help you spread the word – post it on your door in rez or distribute them at your tutorial and attend the best exam prep sessions at McGill: 15h of exam-level questions spread over the 4 weeks leading up to your exam, designed to help you ace the class!

MATH 141 – Quiz 1 – More Sample Questions

Here’s a second set of sample questions from the first of this year’s 141 quizzes. As expected, the general structure appears consistent, but the relative level of difficulty is a bit higher here. For example, the Riemann Sum question doesn’t have lower limit a = 0 which means you really have to have a solid understanding of how to work backwards to identify the function. Thanks to Marco for sharing!

1. Evaluate \displaystyle \lim_{n\rightarrow \infty} \sum_{i = 1}^{n}\sin\left(\frac{\pi}{2} + \frac{\pi i}{2n} \right)\cdot \frac{\pi}{2n}

2. \displaystyle \frac{\text{d}}{\text{d}x} \int_{\sqrt{x}}^4 e^{t^2}\text{d}t =

3. Evaluate the following integrals:

    • \displaystyle \int \frac{\pi}{6+x^2} \text{d}x
    • \displaystyle \int \frac{x+5}{x^2 + 10x - 7}\text{d}x
    • \displaystyle \int_a^{b} \frac{1}{x(1+\ln^2 x)}\text{d}x