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 Indefinite Integrals 28 Flashcards |
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What is the process called that finds anti-derivatives of a function? |
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Integration or anti-differentiation. |
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Integration can be classified into two categories: definite and ___ integrals. |
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Indefinite |
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Evaluate: 
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Use substitution x2=tanθ, we get |
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What is the general formula for an indefinite integral? |
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∫f(x) dx = F(x) + C, where F(x) is the anti-derivative and C is the constant of integration. |
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Let I= |
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What is I?
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Fill in the blank: The integration of a function of the form xp can be expressed through elementary functions only in specific cases when p is a ___ or a ___ number. |
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Integer or rational |
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What does the constant 'C' represent in the context of indefinite integrals? |
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It represents the constant of integration, indicating there are infinitely many anti-derivatives. |
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What is the formula for integration by parts? |
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∫u dv = uv - ∫v du, where u and v are differentiable functions. |
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Fill in the blank: The definite integral is also known as a ___ integral when restricted to the real line. |
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Riemann |
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True or False:
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True |
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What method is used to integrate the product of two functions? |
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Integration by parts. |
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Fill in the blank:
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Card: 24 / 28 |
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Evaluate:
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Which of the following substitutions is best for A) x = a tanθ |
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B) x = a secθ |
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Completed! Keep practicing to master all of them. |
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