Quiz — Primitives_lpbt.pdf

Question 1 sur 10 20:00

[{"id":31250,"question":"Quelle est la primitive de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"A. x³ + x² - x + C","option_b":"B. x³ + x² - x","option_c":"C. 6x + 2 + C","option_d":"D. 3x³ + 2x² - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 3x² est x³, celle de 2x est x², et celle de -1 est -x. On ajoute la constante C.","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 + x² - x + C\", \"b\": \"B. x³ + x² - x\", \"c\": \"C. 6x + 2 +","_debug_options_count":4},{"id":31251,"question":"L'intégrale définie ∫(de 0 à 1) (2x + 1) dx est égale à :","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de 2x + 1 est x² + x. Évaluée entre 0 et 1, on obtient (1 + 1) - (0 + 0) = 2.","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. 1\", \"b\": \"B. 2\", \"c\": \"C. 3\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":31252,"question":"La primitive de e^(2x) est :","option_a":"A. e^(2x) + C","option_b":"B. (1\/2)e^(2x) + C","option_c":"C. 2e^(2x) + C","option_d":"D. e^(x) + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant le changement de variable u = 2x, la primitive devient (1\/2)e^(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. e^(2x) + C\", \"b\": \"B. (1\/2)e^(2x) + C\", \"c\": \"C. 2e^(2x) + C\",","_debug_options_count":4},{"id":31253,"question":"Vrai ou Faux ? La primitive de 1\/x est ln|x| + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale : la primitive de 1\/x est bien ln|x| + C pour x ≠ 0.","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":31254,"question":"Quelle méthode utiliser pour calculer la primitive de x * e^x ?","option_a":"A. Linéarité","option_b":"B. Changement de variable","option_c":"C. Intégration par parties","option_d":"D. Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégration par parties (u = x, dv = e^x dx) est la méthode adaptée pour ce produit de fonctions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. Linéarité\", \"b\": \"B. Changement de variable\", \"c\": \"C. Inté","_debug_options_count":4},{"id":31255,"question":"L'intégrale ∫(de 0 à π) sin(x) dx est égale à :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. π","option_e":"","option_f":"","bonne_reponse":"c","explication":"La primitive de sin(x) est -cos(x). Évaluée entre 0 et π, on obtient -cos(π) - (-cos(0)) = 1 - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\", \"c\": \"C. 2\", \"d\": \"D. π\"}}","_debug_options_count":4},{"id":31256,"question":"Vrai ou Faux ? Toute fonction continue admet une primitive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental de l'analyse : si f est continue sur un intervalle, alors elle admet une primitive sur cet intervalle.","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":31257,"question":"Quelle est la primitive de 1\/(1 + x²) ?","option_a":"A. ln(1 + x²) + C","option_b":"B. arctan(x) + C","option_c":"C. 1\/(1 + x²) + C","option_d":"D. x\/(1 + x²) + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de arctan(x) est 1\/(1 + x²), donc sa primitive est arctan(x) + 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. ln(1 + x²) + C\", \"b\": \"B. arctan(x) + C\", \"c\": \"C. 1\/(1 + x²","_debug_options_count":4},{"id":31258,"question":"Pour calculer ∫ x² * ln(x) dx, quelle méthode est la plus adaptée ?","option_a":"A. Linéarité","option_b":"B. Changement de variable","option_c":"C. Intégration par parties","option_d":"D. Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégration par parties (u = ln(x), dv = x² dx) est la méthode à utiliser pour ce produit de fonctions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. Linéarité\", \"b\": \"B. Changement de variable\", \"c\": \"C. Inté","_debug_options_count":4},{"id":31259,"question":"L'intégrale ∫(de -1 à 1) x³ dx est égale à :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction x³ est impaire et l'intervalle est symétrique autour de 0, donc l'intégrale est nulle.","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. 0\", \"b\": \"B. 1\", \"c\": \"C. 2\", \"d\": \"D. -1\"}}","_debug_options_count":4}]