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Integration Techniques flashcards
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- What does “Antiderivative Power Rule” mean?Antiderivatives
- A function family whose derivative is the given power function.
- What important condition applies to antiderivative power rule?Antiderivatives
- The exponent −1 is an exception to the power shortcut.
- What does “The Reciprocal Exception” mean?Antiderivatives
- The logarithmic antiderivative of a reciprocal input.
- What important condition applies to the reciprocal exception?Antiderivatives
- ln|x| handles negative intervals too; the function remains undefined at zero.
- What does “Substitution with a Nonlinear Input” mean?Substitution
- Changing variables to expose an integrable composition.
- What important condition applies to substitution with a nonlinear input?Substitution
- Do not mix old x bounds with an integrand written in u.
- What does “Substitution with a Linear Input” mean?Substitution
- A change of integration variable using a linear transformation.
- What important condition applies to substitution with a linear input?Substitution
- Account for the derivative of the substituted expression.
- What does “Initial Conditions” mean?Initial-Value Problems
- A specified function value selecting one solution from an antiderivative family.
- What important condition applies to initial conditions?Initial-Value Problems
- The initial condition determines the integration constant.
- What does “Checking a Particular Solution” mean?Initial-Value Problems
- An antiderivative satisfying both a derivative equation and a specified value.
- What important condition applies to checking a particular solution?Initial-Value Problems
- A correct derivative alone does not guarantee the correct initial value.