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Knowledge base
More explainers from the knowledge base. Each one names what you need to know first, works through the method, and says where it usually goes wrong.
Application CalculusWhat Integrals Are Used For in PracticeAn integral answers one question — how much has accumulated — and that question turns out to underlie area, distance, cost and probability alike.
Distinction CalculusDerivative vs Integral: What Each One Actually DoesOne breaks a quantity down into its instantaneous rate of change; the other builds a quantity back up from that rate. Neither makes sense in isolation from the other.
Mistakes Calculus6 Common Integration MistakesFive of the six are caught the same way: differentiate your answer and compare it to the original expression.
Examples CalculusIntegral Examples: 10 Worked ProblemsTen integrals, ordered so each one adds exactly one new idea to the last — and every antiderivative here is checked by differentiating it back.
Formula CalculusIntegral Formulas: The Complete TableOne short table of base cases, and a second showing what happens to each one when the input is a linear expression instead of a bare x.
Method CalculusHow to Integrate: Step by StepIntegration is mostly pattern recognition — matching the shape in front of you to a rule for reversing it, and always checking the result by differentiating back.