Quiz — 7-Définition et premiéres propriétés-Primitive-Exemple d_application.... .pdf

Question 1 sur 10 20:00

[{"id":49227,"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. x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 3x² est obtenue en appliquant la formule : ∫3x² dx = 3*(x³\/3) + C = x³ + 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 + C\", \"b\": \"B. x³\", \"c\": \"C. 6x + C\", \"d\": \"D. x² + C\"}}","_debug_options_count":4},{"id":49228,"question":"La primitive de e^x est-elle e^x + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car la dérivée de e^x est e^x, donc e^x est bien une primitive de e^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":49229,"question":"Quelle est la primitive de f(x) = 5 ?","option_a":"A. 5x + C","option_b":"B. x + C","option_c":"C. 5x² + C","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive d'une constante 5 est 5x + C, car la dérivée de 5x est 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\": \"A. 5x + C\", \"b\": \"B. x + C\", \"c\": \"C. 5x² + C\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":49230,"question":"La primitive de sin(x) est-elle -cos(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car la dérivée de -cos(x) est sin(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":49231,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"A. x⁴ - x² + x + C","option_b":"B. x⁴ - x² + C","option_c":"C. 12x² - 2 + C","option_d":"D. x⁴ - 2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la linéarité et les formules de primitives : ∫4x³ dx = x⁴, ∫-2x dx = -x², ∫1 dx = x. Donc la primitive est x⁴ - x² + x + 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. x⁴ - x² + x + C\", \"b\": \"B. x⁴ - x² + C\", \"c\": \"C. 12x² ","_debug_options_count":4},{"id":49232,"question":"La primitive de 1\/x est-elle ln(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car la dérivée de ln(x) est 1\/x pour x \u003E 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":49233,"question":"Quelle est la primitive de f(x) = cos(2x) ?","option_a":"A. sin(2x)\/2 + C","option_b":"B. -sin(2x)\/2 + C","option_c":"C. 2sin(2x) + C","option_d":"D. sin(2x) + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de cos(2x) est sin(2x)\/2 + C, car la dérivée de sin(2x)\/2 est cos(2x).","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. sin(2x)\/2 + C\", \"b\": \"B. -sin(2x)\/2 + C\", \"c\": \"C. 2sin(2x) + ","_debug_options_count":4},{"id":49234,"question":"La primitive de f(x) = x*e^x est-elle e^x(x - 1) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car en utilisant l'intégration par parties, on obtient e^x(x - 1) + 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":49235,"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\/x + C","option_d":"D. x\/(1 + x²) + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 1\/(1 + x²) est arctan(x) + C, car la dérivée de arctan(x) est 1\/(1 + x²).","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\/x + C\", ","_debug_options_count":4},{"id":49236,"question":"La primitive de f(x) = 1\/√x est-elle 2√x + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car la dérivée de 2√x est 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}]