Maîtrisez les intégrales en Terminale : QCM et Vrai/Faux

Question 1 sur 10 10:00

[{"id":21998,"question":"Quelle est la primitive de la fonction f(x) = 3x² ?","option_a":"x³ + C","option_b":"x³ + 3x + C","option_c":"6x + C","option_d":"x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x² est obtenue en appliquant la formule ∫xⁿ dx = 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":21999,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 1 est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons l'intégrale : ∫(2x + 1) dx = x² + x + C. Entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 2. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22000,"question":"Quelle méthode utiliser pour calculer ∫x eˣ dx ?","option_a":"Intégration par parties","option_b":"Changement de variable","option_c":"Décomposition en éléments simples","option_d":"Primitive directe","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette intégrale se calcule par intégration par parties, en posant u = x et dv = eˣ dx.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22001,"question":"L'intégrale ∫(sin x) dx est égale à -cos x + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de -cos x est sin x, donc ∫(sin x) dx = -cos x + C. L'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22002,"question":"Quelle est la valeur de ∫(1\/x) dx ?","option_a":"ln|x| + C","option_b":"x²\/2 + C","option_c":"eˣ + C","option_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":22003,"question":"L'intégrale ∫(x² + 2x + 1) dx entre -1 et 1 est égale à 8\/3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calculons l'intégrale : ∫(x² + 2x + 1) dx = x³\/3 + x² + x + C. Entre -1 et 1, cela donne (1\/3 + 1 + 1) - (-1\/3 + 1 - 1) = 7\/3. L'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22004,"question":"Quelle est l'aire sous la courbe de f(x) = x² entre 0 et 2 ?","option_a":"8\/3","option_b":"4","option_c":"2","option_d":"16\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire se calcule avec ∫₀² x² dx = [x³\/3]₀² = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22005,"question":"L'intégrale ∫(eˣ) dx est égale à eˣ + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de eˣ est eˣ, donc ∫(eˣ) dx = eˣ + C. L'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22006,"question":"Quelle méthode utiliser pour calculer ∫(x \/ (x² + 1)) dx ?","option_a":"Changement de variable u = x² + 1","option_b":"Intégration par parties","option_c":"Décomposition en éléments simples","option_d":"Primitive directe","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette intégrale se calcule par changement de variable en posant u = x² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22007,"question":"L'intégrale ∫(cos x) dx entre 0 et π\/2 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons l'intégrale : ∫(cos x) dx = sin x + C. Entre 0 et π\/2, cela donne sin(π\/2) - sin(0) = 1 - 0 = 1. L'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]