Quiz — 62d69cd33cbbe_fiche-methodes-primitives.pdf

Question 1 sur 5 10:00

[{"id":101782,"question":"Quelle est la primitive de la fonction f(x) = 3x² + 2x + 1 ?","option_a":"F(x) = x³ + x² + x + C","option_b":"F(x) = 6x + 2 + C","option_c":"F(x) = x³ + x² + 1 + C","option_d":"F(x) = 3x³ + 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive d'une somme de fonctions est la somme des primitives de chaque terme. Pour 3x², la primitive est x³ ; pour 2x, c'est x² ; et pour 1, c'est x. La constante C est ajoutée à la fin.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"F(x) = x³ + x² + x + C\", \"b\": \"F(x) = 6x + 2 + C\", \"c\": \"F(x) =","_debug_options_count":4},{"id":101783,"question":"Quelle méthode utiliser pour calculer ∫x*e^x dx ?","option_a":"Intégration par parties","option_b":"Changement de variable","option_c":"Linéarité de l'intégrale","option_d":"Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégration par parties est adaptée pour les produits de fonctions, notamment quand l'une est une dérivée connue (ici, e^x). La formule est ∫u*v' = u*v - ∫u'*v.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Intégration par parties\", \"b\": \"Changement de variable\", \"c\": \"L","_debug_options_count":4},{"id":101784,"question":"Quelle est la primitive de f(x) = 1\/(1+x²) ?","option_a":"F(x) = arctan(x) + C","option_b":"F(x) = ln(1+x²) + C","option_c":"F(x) = -1\/(1+x²) + C","option_d":"F(x) = x\/(1+x²) + C","option_e":"","option_f":"","bonne_reponse":"a","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\": \"a\", \"options\": {\"a\": \"F(x) = arctan(x) + C\", \"b\": \"F(x) = ln(1+x²) + C\", \"c\": \"F(x) = ","_debug_options_count":4},{"id":101785,"question":"Calculez ∫(2x+3)*e^(x²+3x) dx.","option_a":"F(x) = e^(x²+3x) + C","option_b":"F(x) = 2*e^(x²+3x) + C","option_c":"F(x) = (x²+3x)*e^(x²+3x) + C","option_d":"F(x) = 1\/(x²+3x)*e^(x²+3x) + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"Utilisez le changement de variable u = x²+3x. La dérivée de u est 2x+3, qui est présente dans l'intégrale. Ainsi, ∫e^u du = e^u + 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\": \"F(x) = e^(x²+3x) + C\", \"b\": \"F(x) = 2*e^(x²+3x) + C\", \"c\": \"F(x","_debug_options_count":4},{"id":101786,"question":"Quelle est la primitive de f(x) = sin(2x) ?","option_a":"F(x) = -cos(2x)\/2 + C","option_b":"F(x) = cos(2x)\/2 + C","option_c":"F(x) = -sin(2x) + C","option_d":"F(x) = 2*cos(2x) + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de -cos(2x)\/2 est sin(2x), car la dérivée de cos(2x) est -2*sin(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"F(x) = -cos(2x)\/2 + C\", \"b\": \"F(x) = cos(2x)\/2 + C\", \"c\": \"F(x) =","_debug_options_count":4}]