Integration

What this unit covers

The page lists resources on integration made by GoConqr users. Many are mind maps on strategy and technique. Others are flashcard decks of formulae, plus quizzes, notes, flowcharts and slide sets. Exams mentioned include AP Calculus AB, AP Calculus, A-level Maths and GCSE Maths.

Where to start

Begin with the mind map Integration Strategy. It sets out the basic trigonometric results, such as the integral of sin x being minus cos x plus C, and shows when to manipulate a function before integrating. Then move to Techniques of Integration, which names basic substitution, completing the square, trigonometric identities, by parts, partial fractions and trigonometric substitution.

Next, the Antiderivatives mind map links the ideas to rectilinear motion, area, arc length, volume and the Fundamental Theorem of Calculus. The note Integral Maths - Definite Integrals explains that integration has uses beyond reversing differentiation.

Using quizzes and maps together

Read a map first, then test yourself. Try the quiz Trigonometry Identities and Anti-Derivatives, which asks for results such as the antiderivative of sec²(x). Area Quiz (NO CALCULATOR) and Volume Quiz (NO CALCULATOR) move on to applications. If an answer surprises you, go back to the matching branch of the map.

• Use flashcards such as Integration Formulas for quick recall.
• Use Calculus II Improper Integrals for limits of exponentials.
• Use the AP Exam Integrals (Multiple Choice) AB decks for exam-style practice.

Where it sits

This unit belongs to the Calculus strand of Mathematics, in the Sciences area. Limits and differentiation sit alongside it in the same strand, so the resources here assume you know how derivatives work.

Pick a resource that matches where you are today, and make a map or deck of your own when you want to go further.