Quiz : Maîtrisez les primitives et l'intégration en Terminale

Question 1 sur 10 10:00

[{"id":22888,"question":"Quelle est la primitive de la fonction f(x) = 3x² ?","option_a":"A. x³","option_b":"B. x³ + C","option_c":"C. 6x","option_d":"D. x³ + 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de 3x² est x³ + C, car la dérivée de x³ est 3x². Le +C représente la constante d'intégration.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22889,"question":"La primitive de e^(2x) est (1\/2)e^(2x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. En dérivant (1\/2)e^(2x), on obtient e^(2x) grâce à la règle de la chaîne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22890,"question":"Quelle méthode utilise-t-on pour calculer une primitive de la forme u'(x) * e^(u(x)) ?","option_a":"A. Intégration par parties","option_b":"B. Changement de variable","option_c":"C. Décomposition en éléments simples","option_d":"D. Intégration directe","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise le changement de variable en posant v = u(x), car la dérivée de e^v est e^v * v'.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22891,"question":"La primitive de sin(2x) est :","option_a":"A. -cos(2x)\/2 + C","option_b":"B. cos(2x)\/2 + C","option_c":"C. -2cos(2x) + C","option_d":"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":22892,"question":"L'intégration par parties s'applique à toute fonction dérivable.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. L'intégration par parties s'applique surtout aux produits de fonctions, comme u(x)*v'(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22893,"question":"Quelle est la primitive de 1\/(1+x²) ?","option_a":"A. arctan(x) + C","option_b":"B. ln(1+x²) + C","option_c":"C. x\/(1+x²) + C","option_d":"D. 1\/(1+x²) + 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":22894,"question":"Pour calculer la primitive de x*e^x, quelle méthode utilise-t-on ?","option_a":"A. Intégration 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":"On utilise l'intégration par parties avec u = x et v' = e^x, car cela simplifie le calcul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22895,"question":"La primitive de cos(x) est -sin(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La primitive de cos(x) est sin(x) + C, car la dérivée de sin(x) est cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22896,"question":"Quelle est la primitive de 1\/x pour x \u003E 0 ?","option_a":"A. ln(x) + C","option_b":"B. x*ln(x) + C","option_c":"C. 1\/x² + C","option_d":"D. e^x + 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":22897,"question":"La primitive de u'(x)\/u(x) est ln(|u(x)|) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. En dérivant ln(|u(x)|), on obtient u'(x)\/u(x) grâce à la règle de la chaîne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]