Quiz — Résumé-primitives.pdf

Question 1 sur 10 20:00

[{"id":53207,"question":"Quelle est la primitive de la fonction f(x) = 3x² ?","option_a":"A. x³ + C","option_b":"B. x³","option_c":"C. 6x + C","option_d":"D. 3x³ + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 3x² est x³ + C car la dérivée de x³ est 3x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x³ + C\", \"b\": \"B. x³\", \"c\": \"C. 6x + C\", \"d\": \"D. 3x³ + C\"}","_debug_options_count":4},{"id":53208,"question":"La fonction F(x) = 2x + 5 est une primitive de f(x) = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de F(x) = 2x + 5 est f(x) = 2, donc F est bien une primitive de f.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":53209,"question":"Quelle méthode utiliser pour calculer ∫x·eˣ dx ?","option_a":"A. Primitive directe","option_b":"B. Intégration par parties","option_c":"C. Changement de variable","option_d":"D. Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégration par parties est adaptée car il s'agit d'un produit de fonctions (x et eˣ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. Primitive directe\", \"b\": \"B. Intégration par parties\", \"c\": \"","_debug_options_count":4},{"id":53210,"question":"La primitive de f(x) = 1\/x est ln|x| + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln|x| est 1\/x, donc ln|x| + C est bien une primitive de 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":53211,"question":"Quelle est la primitive de f(x) = sin(2x) ?","option_a":"A. -cos(2x) + C","option_b":"B. -2cos(2x) + C","option_c":"C. (1\/2)cos(2x) + C","option_d":"D. -cos(x) + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de -2cos(2x) est 4sin(2x), donc la primitive de sin(2x) est -(1\/2)cos(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. -cos(2x) + C\", \"b\": \"B. -2cos(2x) + C\", \"c\": \"C. (1\/2)cos(2x) ","_debug_options_count":4},{"id":53212,"question":"La primitive de f(x) = e^(3x) est e^(3x)\/3 + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(3x)\/3 est e^(3x), donc e^(3x)\/3 + C est bien une primitive de e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":53213,"question":"Quelle est la primitive de f(x) = 1\/(1+x²) ?","option_a":"A. arctan(x) + C","option_b":"B. ln(1+x²) + C","option_c":"C. 1\/(1+x²) + C","option_d":"D. x\/(1+x²) + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de arctan(x) est 1\/(1+x²), donc arctan(x) + C est la primitive recherchée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. arctan(x) + C\", \"b\": \"B. ln(1+x²) + C\", \"c\": \"C. 1\/(1+x²) + ","_debug_options_count":4},{"id":53214,"question":"La primitive de f(x) = cos(x) est sin(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est cos(x), donc sin(x) + C est bien une primitive de cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":53215,"question":"Quelle méthode utiliser pour calculer ∫x²·ln(x) dx ?","option_a":"A. Primitive directe","option_b":"B. Intégration par parties","option_c":"C. Changement de variable","option_d":"D. Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégration par parties est adaptée car il s'agit d'un produit de fonctions (x² et ln(x)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. Primitive directe\", \"b\": \"B. Intégration par parties\", \"c\": \"","_debug_options_count":4},{"id":53216,"question":"La primitive de f(x) = 5 est 5x + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 5x + C est 5, donc 5x + C est bien une primitive de 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]