Quiz : Maîtrisez les intégrales en Terminale Mathématiques

Question 1 sur 10 10:00

[{"id":63142,"question":"Quelle est la primitive de la fonction f(x) = 3x² ?","option_a":"x³","option_b":"x³ + C","option_c":"6x","option_d":"x² + C","option_e":"","option_f":"","bonne_reponse":"B","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":63143,"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":"L'intégrale ∫(2x + 1) dx est bien x² + x + C, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63144,"question":"Quelle méthode utiliser pour calculer ∫x·eˣ dx ?","option_a":"Intégration directe","option_b":"Intégration par parties","option_c":"Changement de variable","option_d":"Décomposition en éléments simples","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégration par parties est adaptée pour les produits de fonctions comme x·eˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63145,"question":"L'intégrale ∫(1\/x) dx est égale à ln|x| + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est bien ln|x| + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63146,"question":"Calculer ∫sin(2x) dx.","option_a":"-cos(2x)\/2 + C","option_b":"cos(2x)\/2 + C","option_c":"-2cos(2x) + C","option_d":"sin(2x)\/2 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de sin(2x) est -cos(2x)\/2 + C, car la dérivée de -cos(2x)\/2 est sin(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63147,"question":"Quelle est la valeur de ∫₀¹ (3x² + 2x) dx ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale vaut [x³ + x²]₀¹ = 1 + 1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63148,"question":"L'intégrale ∫e^(3x) dx peut se calculer par un changement de variable.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En posant u = 3x, on obtient ∫e^u (du\/3) = e^(3x)\/3 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63149,"question":"Quelle est la primitive de f(x) = 1\/(x² + 1) ?","option_a":"arctan(x) + C","option_b":"ln(x² + 1) + C","option_c":"x² + C","option_d":"1\/(x + 1) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/(x² + 1) est arctan(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63150,"question":"Calculer ∫x·ln(x) dx.","option_a":"(x²\/2)·ln(x) - x²\/4 + C","option_b":"x·ln(x) - x + C","option_c":"x²·ln(x) + C","option_d":"(x²\/2)·ln(x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant l'intégration par parties, on obtient (x²\/2)·ln(x) - x²\/4 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":63151,"question":"L'intégrale ∫₀ᵖⁱ sin(x) dx est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de sin(x) sur [0, π] est [-cos(x)]₀ᵖⁱ = -(-1) - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]