Quiz : Maîtrisez les primitives et intégrales en Terminale Math

Question 1 sur 10 10:00

[{"id":26998,"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 xⁿ est x^(n+1)\/(n+1) + C. Ici, n=2, donc la primitive est x³ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26999,"question":"L'intégrale ∫(2x + 1) dx est égale à x² + x + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant x² + x + C, on obtient 2x + 1, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27000,"question":"Quelle méthode utiliser pour calculer ∫x * e^x dx ?","option_a":"A. Substitution simple","option_b":"B. Intégration par parties","option_c":"C. Décomposition en éléments simples","option_d":"D. Changement de variable","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégration par parties (u = x, dv = e^x dx) est la méthode adaptée pour les produits de fonctions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27001,"question":"L'intégrale définie ∫(de 0 à 1) x² dx représente :","option_a":"A. La longueur de la courbe y = x² entre 0 et 1","option_b":"B. L'aire sous la courbe y = x² entre 0 et 1","option_c":"C. Le volume d'un solide de révolution","option_d":"D. La dérivée de x²","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une intégrale définie entre a et b représente l'aire algébrique sous la courbe de la fonction entre ces deux points.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27002,"question":"La primitive de 1\/(1+x²) est arctan(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de arctan(x) est 1\/(1+x²), donc la primitive est bien arctan(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27003,"question":"Quelle est la primitive de sin(2x) ?","option_a":"A. -cos(2x) + C","option_b":"B. -2cos(2x) + C","option_c":"C. cos(2x) + C","option_d":"D. -1\/2 cos(2x) + C","option_e":"","option_f":"","bonne_reponse":"D","explication":"En utilisant la formule ∫sin(ax) dx = -1\/a cos(ax) + C, on obtient -1\/2 cos(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27004,"question":"L'intégrale ∫(de 0 à π) sin(x) dx est égale à :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. π","option_e":"","option_f":"","bonne_reponse":"C","explication":"La primitive de sin(x) est -cos(x). Évaluée entre 0 et π, on obtient -cos(π) - (-cos(0)) = 1 - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27005,"question":"La méthode de substitution est utile pour intégrer des fonctions de la forme f(g(x)) * g'(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est exactement le principe de la substitution : poser u = g(x), alors du = g'(x) dx.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27006,"question":"Quelle est la primitive de e^(3x) ?","option_a":"A. e^(3x) + C","option_b":"B. 1\/3 e^(3x) + C","option_c":"C. 3e^(3x) + C","option_d":"D. e^(3x+1) + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule ∫e^(ax) dx = 1\/a e^(ax) + C, on obtient 1\/3 e^(3x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27007,"question":"L'intégrale ∫(de -1 à 1) x³ dx est égale à :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction x³ est impaire, donc l'intégrale entre -1 et 1 est nulle (aires opposées).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]