Quiz — 63becdaf33f74_énoncé_Série 11-Top50-Primitive (1).pdf

Question 1 sur 10 20:00

[{"id":58172,"question":"Quelle est la primitive de 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":58173,"question":"L'intégrale ∫[0,1] (2x + 1) dx est égale à :","option_a":"A) 1","option_b":"B) 2","option_c":"C) 3","option_d":"D) 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une primitive de 2x + 1 est x² + x. Évaluée entre 0 et 1 : (1² + 1) - (0² + 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) 0\"}}","_debug_options_count":4},{"id":58174,"question":"Vrai ou Faux ? Toute fonction continue sur un intervalle admet une primitive sur cet intervalle.","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 [a,b], 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":58175,"question":"Quelle méthode utiliser pour calculer ∫ x e^x dx ?","option_a":"A) Intégration par substitution","option_b":"B) Intégration par parties","option_c":"C) Décomposition en éléments simples","option_d":"D) Linéarité de l'intégrale","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule d'intégration par parties (u'v + uv') est adaptée pour les produits de fonctions comme x e^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) Intégration par substitution\", \"b\": \"B) Intégration par part","_debug_options_count":4},{"id":58176,"question":"L'intégrale ∫[1,2] (1\/x) dx est égale à :","option_a":"A) ln(2)","option_b":"B) ln(2) - ln(1)","option_c":"C) 1","option_d":"D) 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une primitive de 1\/x est ln(x). Évaluée entre 1 et 2 : ln(2) - ln(1) = ln(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) ln(2)\", \"b\": \"B) ln(2) - ln(1)\", \"c\": \"C) 1\", \"d\": \"D) 0\"}}","_debug_options_count":4},{"id":58177,"question":"Vrai ou Faux ? Si F est une primitive de f, alors ∫[a,b] f(x)dx = F(a) - F(b).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est l'inverse : ∫[a,b] f(x)dx = F(b) - F(a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":58178,"question":"Quelle est la primitive de f(x) = e^(2x) ?","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 la substitution u = 2x, on obtient (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":58179,"question":"L'intégrale ∫[0,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":"Une primitive de sin(x) est -cos(x). Évaluée entre 0 et π : -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":58180,"question":"Vrai ou Faux ? La primitive d'une fonction constante est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive d'une constante k est kx + C, qui est une fonction affine.","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":58181,"question":"Quelle est la valeur de ∫[0,1] x² dx ?","option_a":"A) 1\/3","option_b":"B) 1\/2","option_c":"C) 1","option_d":"D) 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une primitive de x² est (1\/3)x³. Évaluée entre 0 et 1 : (1\/3)(1³) - (1\/3)(0³) = 1\/3.","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) 1\/3\", \"b\": \"B) 1\/2\", \"c\": \"C) 1\", \"d\": \"D) 2\"}}","_debug_options_count":4}]