Quiz : Maîtrisez les primitives en mathématiques

Question 1 sur 10 10:00

[{"id":71812,"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 utilisant la règle de puissance : ∫3x² dx = 3*(x³\/3) + C = x³ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71813,"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},{"id":71814,"question":"Quelle est la primitive de f(x) = 1\/x ?","option_a":"A) ln|x| + C","option_b":"B) x + C","option_c":"C) -1\/x² + C","option_d":"D) 1\/x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est ln|x| + C, car la dérivée de ln|x| est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71815,"question":"La primitive de sin(x) est cos(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de sin(x) est -cos(x) + C, car la dérivée de -cos(x) est sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71816,"question":"Quelle est la primitive de f(x) = 5x⁴ ?","option_a":"A) x⁵ + C","option_b":"B) 5x⁵ + C","option_c":"C) x⁴ + C","option_d":"D) 20x³ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de puissance, ∫5x⁴ dx = 5*(x⁵\/5) + C = x⁵ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71817,"question":"La primitive de cos(x) est 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 sa primitive est bien sin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71818,"question":"Quelle est la primitive de f(x) = 2x + 1 ?","option_a":"A) x² + x + C","option_b":"B) x² + C","option_c":"C) 2x² + x + C","option_d":"D) x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En intégrant terme à terme, ∫(2x + 1) dx = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71819,"question":"La primitive de ln(x) est 1\/x + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de ln(x) est x*ln(x) - x + C, car sa dérivée est ln(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71820,"question":"Quelle est la primitive de f(x) = e^(2x) ?","option_a":"A) (1\/2)e^(2x) + C","option_b":"B) e^(2x) + C","option_c":"C) 2e^(2x) + C","option_d":"D) e^x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la méthode de substitution, ∫e^(2x) dx = (1\/2)e^(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71821,"question":"La primitive de tan(x) est -ln|cos(x)| + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de -ln|cos(x)| est tan(x), donc sa primitive est bien -ln|cos(x)| + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]