Quiz : Maîtrisez l'intégration en 10 questions !

Question 1 sur 10 10:00

[{"id":48961,"question":"Quelle est la primitive de la fonction f(x) = 3x² ?","option_a":"A. x³ + C","option_b":"B. 6x + C","option_c":"C. x² + C","option_d":"D. 3x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x² est obtenue en appliquant la règle de la primitive d'une fonction puissance : ∫3x² dx = 3*(x³\/3) + C = x³ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48962,"question":"L'intégrale ∫₀¹ (2x + 1) dx est égale à :","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calculons la primitive de 2x + 1 : F(x) = x² + x. Ensuite, F(1) - F(0) = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48963,"question":"Vrai ou Faux ? La dérivée d'une primitive est la fonction originale.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est exact : si F est une primitive de f, alors F' = f.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48964,"question":"Quelle est la primitive de la fonction f(x) = e^(2x) ?","option_a":"A. e^(2x) + C","option_b":"B. (1\/2)e^(2x) + C","option_c":"C. 2e^(2x) + C","option_d":"D. e^x + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de e^(2x) est (1\/2)e^(2x) + C, car la dérivée de (1\/2)e^(2x) est e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48965,"question":"L'aire sous la courbe de f(x) = x² entre x = 0 et x = 2 est égale à :","option_a":"A. 4\/3","option_b":"B. 8\/3","option_c":"C. 2","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calculons l'intégrale ∫₀² x² dx = [x³\/3]₀² = 8\/3 - 0 = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48966,"question":"Vrai ou Faux ? ∫(sin(x) + cos(x)) dx = -cos(x) + sin(x) + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : la primitive de sin(x) est -cos(x) et celle de cos(x) est sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48967,"question":"Quelle est la primitive de la fonction f(x) = 1\/(1 + x²) ?","option_a":"A. ln(1 + x²) + C","option_b":"B. arctan(x) + C","option_c":"C. 1\/(1 + x²) + C","option_d":"D. x\/(1 + x²) + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de 1\/(1 + x²) est arctan(x) + C, une formule à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48968,"question":"L'intégrale ∫₀^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). Donc ∫₀^π sin(x) dx = -cos(π) - (-cos(0)) = 1 - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48969,"question":"Vrai ou Faux ? L'intégrale d'une somme de fonctions est égale à la somme des intégrales.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : ∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48970,"question":"Quelle est la primitive de la fonction f(x) = 1\/x (pour x \u003E 0) ?","option_a":"A. ln(x) + C","option_b":"B. 1\/x² + C","option_c":"C. x + C","option_d":"D. e^x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est ln(x) + C, une formule fondamentale à retenir.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]