d0d-46a7-b619-fb3be822efb9","topicSlug":"integration-2","cards":[{"id":"f51f17a8-913c-4749-b68d-3ea0def23300","cardType":"basic","front":"Which process reverses differentiation?","back":"Integration.","points":1,"mcqOptions":null},{"id":"13944e53-07fd-4d25-b0e2-61621a09a934","cardType":"cloze","front":"If $F'(x)=f(x)$, then $F(x)$ is an [ ] of $f(x)$.","back":"If $F'(x)=f(x)$, then $F(x)$ is an antiderivative of $f(x)$.","points":null,"mcqOptions":null},{"id":"30617512-5b75-449f-b1fd-83de8261bb46","cardType":"basic","front":"In $\\int f(x)\\,dx$, what is $f(x)$ called?","back":"The integrand.","points":1,"mcqOptions":null},{"id":"490f1dfe-a15a-44e9-a299-1763a60467c2","cardType":"basic","front":"In $\\int f(x)\\,dx$, what does $dx$ indicate?","back":"Integration is with respect to $x$.","points":1,"mcqOptions":null},{"id":"ef529a81-0d7f-4cf3-af7a-d72812c6e702","cardType":"cloze","front":"An indefinite integral represents the complete [ ].","back":"An indefinite integral represents the complete family of antiderivatives.","points":null,"mcqOptions":null},{"id":"04085d96-623c-41f8-810b-54e34f066829","cardType":"basic","front":"Why must an indefinite integral include $+C$?","back":"Differentiation eliminates constants, so the original constant is unknown.","points":2,"mcqOptions":null},{"id":"fc974834-2316-4817-ac5a-19dffc4266d8","cardType":"basic","front":"How does changing $C$ affect the graph of $F(x)+C$?","back":"It causes a vertical translation.","points":1,"mcqOptions":null},{"id":"f49d25e5-169f-49c4-ac60-a6b34fbfac61","cardType":"cloze","front":"For $n\\neq-1$, $\\displaystyle \\int x^n\\,dx=$ $\\text{[...]}$.","back":"For $n\\neq-1$, $\\displaystyle \\int x^n\\,dx=$ $\\boxed{\\displaystyle \\frac{x^{n+1}}{n+1}+C}$.","points":null,"mcqOptions":null},{"id":"d974b389-faa4-4a37-88b8-626c8cdc2a34","cardType":"basic","front":"How is the integration power rule applied to $x^n$?","back":"Add one to the exponent, then divide by the new exponent.","points":2,"mcqOptions":null},{"id":"d4fff077-98b9-4276-b535-9c9229302c46","cardType":"basic","front":"Why does the usual power rule fail for $x^{-1}$?","back":"The new exponent is zero, causing division by zero.","points":2,"mcqOptions":null},{"id":"169440ce-7281-40ae-95d1-b6e8868a8a89","cardType":"basic","front":"Find $\\displaystyle \\int x^5\\,dx$.","back":"$\\displaystyle \\frac{x^6}{6}+C$","points":1,"mcqOptions":null},{"id":"5bfcb46a-0307-41db-9b15-b09b5d58e378","cardType":"basic","front":"Find $\\displaystyle \\int 12x^3\\,dx$.","back":"$3x^4+C$","points":1,"mcqOptions":null},{"id":"23b84466-e782-4aa2-ae76-e3431df06312","cardType":"cloze","front":"A constant coefficient remains a [ ] during integration.","back":"A constant coefficient remains a multiplier during integration.","points":null,"mcqOptions":null},{"id":"a75e92a2-fca4-4e18-bf5f-e50ac048c3ea","cardType":"basic","front":"Find $\\displaystyle \\int k\\,dx$, where $k$ is constant.","back":"$kx+C$","points":1,"mcqOptions":null},{"id":"e127b62f-eb46-4313-ae58-ec9c46b7af88","cardType":"cloze","front":"A sum or difference is integrated [ ].","back":"A sum or difference is integrated term by term.","points":null,"mcqOptions":null},{"id":"16a61845-905a-470e-a271-c818a3b56b62","cardType":"basic","front":"Why is only one $+C$ needed after integrating several terms?","back":"Sepa

1.7.1 Integration Flashcards

1.7.1 Integration Flashcards