An {{CMD_51}}, also called an {{CMD_52}} computes accumulated area: {{MATH_53}} This is a function of {{MATH_54}} whose derivative is {{MATH_55}}, with the additional property that {{MATH_56}}. Pay attention to the notation: {{CMD_57}} {{ENV_58}} {{CMD_59}} Where {{MATH_60}}. {{CMD_61}}{{COMMENT_62}} Accumulation functions {{CMD_63}}{{CMD_64}}have{{CMD_65}}{{CMD_66}}do not have{{CMD_67}}{{CMD_68}} limits of integration, and they compute {{CMD_69}}{{CMD_70}}signed area{{CMD_71}}{{CMD_72}}an antiderivative{{CMD_73}}{{CMD_74}}a class of antiderivatives{{CMD_75}}{{CMD_76}}. {{CMD_77}} {{CMD_78}} True or false: There exists a function {{MATH_79}} such that {{MATH_80}} {{CMD_81}} {{CMD_82}} {{CMD_83}}true{{CMD_84}} {{CMD_85}}false{{CMD_86}} {{CMD_87}} {{CMD_88}} Let {{MATH_89}} this is an accumulation function and {{MATH_90}}, since no area is accumulated yet. However, {{MATH_91}}. Hence there can be no such function {{MATH_92}}. On the other hand, there is a function {{MATH_93}} with {{MATH_94}} namely, {{MATH_95}}. This subtlety arises from the fact that an accumulation function {{MATH_96}} gives a {{CMD_97}}specific{{CMD_98}} antiderivative of {{MATH_99}}, the one that when evaluated at {{MATH_100}} is zero. {{CMD_101}} {{CMD_102}} {{CMD_103}}