Quiz : Maîtrisez les primitives et les intégrales en Terminale Math

Question 1 sur 10 10:00

[{"id":24118,"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 règle de puissance inverse : ∫3x² dx = 3*(x³\/3) + C = x³ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24119,"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":"Oui, car la dérivée de e^x + C est e^x, donc e^x est bien une primitive de e^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24120,"question":"Quelle est la primitive de la fonction f(x) = 1\/x ?","option_a":"A. ln|x| + C","option_b":"B. x + C","option_c":"C. 1\/x² + C","option_d":"D. e^x + 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":24121,"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":"A","explication":"Vrai, car la dérivée de -cos(x) + C est sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24122,"question":"Quelle est la primitive de la fonction 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 est la constante multipliée par x : ∫5 dx = 5x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24123,"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":"Vrai, car la dérivée de sin(x) + C est cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24124,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"A. x⁴ - x² + x + C","option_b":"B. 12x² - 2 + C","option_c":"C. 4x⁴ - 2x² + x + C","option_d":"D. x³ - x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de puissance inverse à chaque terme : ∫(4x³ - 2x + 1) dx = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24125,"question":"La primitive de ln(x) est x*ln(x) - 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 x*ln(x) - x + C est ln(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24126,"question":"Quelle est la primitive de la fonction f(x) = 2e^(2x) ?","option_a":"A. e^(2x) + C","option_b":"B. 4e^(2x) + C","option_c":"C. e^(2x)\/2 + C","option_d":"D. 2e^(2x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la règle de dérivation inverse des fonctions exponentielles : ∫2e^(2x) dx = e^(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24127,"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":"Vrai, car la dérivée de -ln|cos(x)| + C est tan(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]