Quiz : Maîtrisez les primitives en Mathématiques (3ème année secondaire)

Question 1 sur 10 10:00

[{"id":40115,"question":"Quelle est la primitive de 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 ∫x^n dx = (x^(n+1))\/(n+1) + C. Ici, n=2, donc ∫3x² dx = 3*(x³\/3) + C = x³ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40116,"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":"Vrai. 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":40117,"question":"Quelle méthode utiliser pour calculer ∫x*e^x dx ?","option_a":"A : Intégration par parties","option_b":"B : Changement de variable","option_c":"C : Linéarité de l'intégrale","option_d":"D : Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"A","explication":"L’intégration par parties est la méthode adaptée pour ∫x*e^x dx, car elle permet de simplifier le produit de deux fonctions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40118,"question":"La primitive de 1\/(1+x²) est :","option_a":"A : arctan(x) + C","option_b":"B : ln(1+x²) + C","option_c":"C : 2x\/(1+x²) + C","option_d":"D : x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/(1+x²) est arctan(x) + C, car la dérivée de arctan(x) est 1\/(1+x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40119,"question":"Peut-on calculer une primitive de sin(x) sans utiliser de formule ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La primitive de sin(x) est -cos(x) + C, une formule qu’il faut connaître ou retrouver par dérivation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40120,"question":"Quelle est la primitive de f(x) = 5 ?","option_a":"A : 5x + C","option_b":"B : 5 + C","option_c":"C : x + C","option_d":"D : 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive d’une constante est la constante multipliée par x, donc ∫5 dx = 5x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40121,"question":"La primitive de ln(x) est :","option_a":"A : x*ln(x) - x + C","option_b":"B : ln(x)\/x + C","option_c":"C : x + C","option_d":"D : 1\/x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de ln(x) est x*ln(x) - x + C, obtenue par intégration par parties.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40122,"question":"L’intégrale ∫(2x+1)dx est égale à :","option_a":"A : x² + x + C","option_b":"B : 2x² + x + C","option_c":"C : x + C","option_d":"D : 2x + 1 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la linéarité de l’intégrale, ∫(2x+1)dx = 2∫x dx + ∫1 dx = 2*(x²\/2) + x + C = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40123,"question":"La primitive de cos(2x) est :","option_a":"A : sin(2x)\/2 + C","option_b":"B : 2sin(2x) + C","option_c":"C : -sin(2x)\/2 + C","option_d":"D : sin(x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de cos(2x) est sin(2x)\/2 + C, car la dérivée de sin(2x)\/2 est cos(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40124,"question":"Peut-on calculer une primitive de 1\/sqrt(1-x²) sans formule ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La primitive de 1\/sqrt(1-x²) est arcsin(x) + C, une formule à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]