Quiz — série 11 primitive.pdf

Question 1 sur 10 20:00

[{"id":30100,"question":"Quelle est la primitive de la fonction f(x) = 3x² + 2x + 1 ?","option_a":"x³ + x² + x + C","option_b":"x³ + x² + C","option_c":"3x³ + x² + x + C","option_d":"x³ + 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\": \"x³ + x² + x + C\", \"b\": \"x³ + x² + C\", \"c\": \"3x³ + x² + x + ","_debug_options_count":4},{"id":30101,"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":"La dérivée de e^x est e^x, donc sa primitive est bien e^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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30102,"question":"Quelle est la primitive de f(x) = 1\/x (pour x \u003E 0) ?","option_a":"ln(x) + C","option_b":"x² + C","option_c":"1\/x² + C","option_d":"e^x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, donc sa primitive est ln(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\": \"ln(x) + C\", \"b\": \"x² + C\", \"c\": \"1\/x² + C\", \"d\": \"e^x + C\"}}","_debug_options_count":4},{"id":30103,"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":"La dérivée de -cos(x) est sin(x), donc la primitive de sin(x) est bien -cos(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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30104,"question":"Quelle est la primitive de f(x) = 5e^(2x) ?","option_a":"5e^(2x)\/2 + C","option_b":"5e^(2x) + C","option_c":"e^(2x)\/2 + C","option_d":"10e^(2x) + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise la formule de primitive de e^(ax) : (1\/a)e^(ax) + C. Ici a=2, donc 5e^(2x)\/2 + 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\": \"5e^(2x)\/2 + C\", \"b\": \"5e^(2x) + C\", \"c\": \"e^(2x)\/2 + C\", \"d\": \"10","_debug_options_count":4},{"id":30105,"question":"La primitive de f(x) = cos(x) est-elle 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 la primitive de cos(x) est bien sin(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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30106,"question":"Quelle est la primitive de f(x) = 4x³ - 3x² + 2x - 1 ?","option_a":"x⁴ - x³ + x² - x + C","option_b":"x⁴ - x³ + x² - 1 + C","option_c":"4x⁴ - 3x³ + 2x² - x + C","option_d":"x⁴ - x³ + x² - x","option_e":"","option_f":"","bonne_reponse":"a","explication":"Primitive de 4x³ est x⁴, de -3x² est -x³, de 2x est x², et de -1 est -x. On ajoute 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\": \"x⁴ - x³ + x² - x + C\", \"b\": \"x⁴ - x³ + x² - 1 + C\", \"c\": ","_debug_options_count":4},{"id":30107,"question":"La primitive de f(x) = 1\/(1+x²) est-elle arctan(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de arctan(x) est 1\/(1+x²), donc sa primitive est bien arctan(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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30108,"question":"Quelle est la primitive de f(x) = 2\/(x+3) (pour x \u003E -3) ?","option_a":"2ln(x+3) + C","option_b":"ln(2x+6) + C","option_c":"2\/(x+3)² + C","option_d":"2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise la primitive de 1\/(x+a) qui est ln|x+a| + C. Ici a=3, donc 2ln(x+3) + 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\": \"2ln(x+3) + C\", \"b\": \"ln(2x+6) + C\", \"c\": \"2\/(x+3)² + C\", \"d\": \"2","_debug_options_count":4},{"id":30109,"question":"La primitive de f(x) = 3cos(3x) est-elle sin(3x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de sin(3x) est 3cos(3x), donc la primitive de 3cos(3x) est sin(3x) + C. La réponse proposée est donc fausse.","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}]