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MATHS 105

Free study notes for MATHS 105 (MATHS105), one topic at a time, each with worked examples and a practice quiz.

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Course Syllabus

  1. Fundamental Theorem of Calculus (Part 1)
  2. Fundamental Theorem of Calculus (Part 2)
  3. Improper Integrals (Type 1 & 2)
  4. Comparison Test for Improper Integrals
  5. Applications of Definite Integrals: Areas
  6. Vector Algebra and Properties

Study Notes

Fundamental Theorem of Calculus (Part 1)

FTC1 is a foundational concept in calculus because it establishes the relationship between the two main branches: differential calculus (rates of change) and integral calculus (accumulation).

Let's say you have a continuous function $f(t)$. If you define a new function $F(x)$ as the accumulated area under $f(t)$ from a constant $a$ to a variable $x$, like this:

$F(x) = \int_{a}^{x} f(t) dt$

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Applications of Definite Integrals: Areas

Definite integrals are fantastic for finding the area of irregular shapes that can be bounded by functions. The core idea is to find the function that describes the "top" boundary and the "bottom" boundary (or "right" and "left"), and then integrate the difference between them over the desired interval.

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MATHS 105: common questions

What does MATHS 105 cover?

This MATHS 105 study guide covers 6 topics: Fundamental Theorem of Calculus (Part 1), Fundamental Theorem of Calculus (Part 2), Improper Integrals (Type 1 & 2), Comparison Test for Improper Integrals, Applications of Definite Integrals: Areas, Vector Algebra and Properties.

Are these MATHS 105 notes free?

Yes. Every MATHS 105 note on this page is free to read without an account. A free account adds practice quizzes, flashcards and a revision plan.

How do I revise for my MATHS 105 exam?

Read the MATHS 105 note for each topic, then take its practice quiz: the questions you get wrong come back as flashcards until you know them. Save the course to get a revision plan built around your exam date.