{"id":5594,"date":"2019-04-02T22:15:12","date_gmt":"2019-04-02T21:15:12","guid":{"rendered":"http:\/\/mathsguyon.fr\/?page_id=5594"},"modified":"2019-06-05T20:27:41","modified_gmt":"2019-06-05T19:27:41","slug":"le-calcul-integral","status":"publish","type":"page","link":"https:\/\/mathsguyon.fr\/?page_id=5594","title":{"rendered":"Le calcul int\u00e9gral"},"content":{"rendered":"

Les fondamentaux pour le Bac :<\/span><\/h1>\n

1. D\u00e9terminer une primitive de la fonction $$f$$ suivante :<\/h2>\n
    \n
  1. \n

    $$f(x)=2 e^{2x}$$\u00a0 Correction<\/a><\/h2>\n<\/li>\n
  2. \n

    $$f(x)=3 e^{x+3}$$ Correction<\/a><\/h2>\n<\/li>\n
  3. \n

    $$f(x)=e^{-0,2x}$$ Correction<\/a><\/h2>\n<\/li>\n
  4. \n

    $$f(x)=xe^{x^{2}}$$ Correction<\/a><\/h2>\n<\/li>\n<\/ol>\n

    2. Calculer :<\/h2>\n
      \n
    1. \n

      Calculer $$\\displaystyle\\int_{1}^33x^{2}-4x+1\\:\\text{d}x$$ Correction<\/a><\/h2>\n<\/li>\n
    2. \n

      Calculer $$\\displaystyle\\int_{0}^3 e^{x}+x-1\\:\\text{d}x$$\u00a0 Correction<\/a><\/h2>\n<\/li>\n
    3. \n

      Calculer $$\\displaystyle\\int_{1}^3 e^{-x}\\:\\text{d}x$$. Correction<\/a><\/h2>\n<\/li>\n<\/ol>\n

      3. Soit $$F$$, la fonction d\u00e9finie sur $$\\mathbb{R}$$ par $$F(x)=(-2x-1) e^{-2x}$$<\/h2>\n

      Montrer que la fonction $$F$$,\u00a0 est une primitive de la fonction $$f$$ d\u00e9finie par $$f(x)=4xe^{-2x}$$<\/h2>\n

      En d\u00e9duire $$\\displaystyle\\int_{0}^3 4xe^{-2x}\\:\\text{d}x$$.<\/h2>\n

      Aide pour d\u00e9marrer<\/a>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Correction compl\u00e8te<\/a><\/h2>\n

      4. Que peut-on d\u00e9duire pour toutes les primitives de la fonction $$f$$ sur l’intervalle [0;18] ?<\/h2>\n

      \"\"<\/h2>\n

      Correction<\/a><\/h2>\n","protected":false},"excerpt":{"rendered":"

      Les fondamentaux pour le Bac : 1. D\u00e9terminer une primitive de la fonction $$f$$ suivante : $$f(x)=2 e^{2x}$$\u00a0 Correction $$f(x)=3 e^{x+3}$$ Correction $$f(x)=e^{-0,2x}$$ Correction $$f(x)=xe^{x^{2}}$$ Correction 2. Calculer : Calculer $$\\displaystyle\\int_{1}^33x^{2}-4x+1\\:\\text{d}x$$ Correction Calculer $$\\displaystyle\\int_{0}^3 e^{x}+x-1\\:\\text{d}x$$\u00a0 Correction Calculer $$\\displaystyle\\int_{1}^3 e^{-x}\\:\\text{d}x$$. Correction … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":5064,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5594","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5594","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5594"}],"version-history":[{"count":25,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5594\/revisions"}],"predecessor-version":[{"id":5831,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5594\/revisions\/5831"}],"up":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/5064"}],"wp:attachment":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}