Quiz : Maîtrisez les primitives en Terminale Scientifique !

Question 1 sur 10 10:00

[{"id":56091,"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. 3x³ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x² est x³ + C car la dérivée de x³ est 3x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56092,"question":"La fonction F(x) = 2x + 5 est une primitive de f(x) = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de F(x) = 2x + 5 est f(x) = 2, donc F est bien une primitive de f.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56093,"question":"Quelle méthode utiliser pour calculer ∫x·eˣ dx ?","option_a":"A. Primitive directe","option_b":"B. Intégration par parties","option_c":"C. Changement de variable","option_d":"D. Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégration par parties est adaptée car il s'agit d'un produit de fonctions (x et eˣ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56094,"question":"La primitive de f(x) = 1\/x est ln|x| + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln|x| est 1\/x, donc ln|x| + C est bien une primitive de 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56095,"question":"Quelle est la primitive de f(x) = sin(2x) ?","option_a":"A. -cos(2x) + C","option_b":"B. -2cos(2x) + C","option_c":"C. (1\/2)cos(2x) + C","option_d":"D. -cos(x) + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de -2cos(2x) est 4sin(2x), donc la primitive de sin(2x) est -(1\/2)cos(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56096,"question":"La primitive de f(x) = e^(3x) est e^(3x)\/3 + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(3x)\/3 est e^(3x), donc e^(3x)\/3 + C est bien une primitive de e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56097,"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\/(1+x²) + C","option_d":"D. x\/(1+x²) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de arctan(x) est 1\/(1+x²), donc arctan(x) + C est la primitive recherchée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56098,"question":"La primitive de f(x) = 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 sin(x) + C est bien une primitive de cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56099,"question":"Quelle méthode utiliser pour calculer ∫x²·ln(x) dx ?","option_a":"A. Primitive directe","option_b":"B. Intégration par parties","option_c":"C. Changement de variable","option_d":"D. Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégration par parties est adaptée car il s'agit d'un produit de fonctions (x² et ln(x)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56100,"question":"La primitive de f(x) = 5 est 5x + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 5x + C est 5, donc 5x + C est bien une primitive de 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]