The Difference and Connection between Antiderivative and Integral<\/p>\n
The antiderivative is the inverse process of the derivative.The\u00a0integral is to calculate the area closed by the graph of a function and x(or y) axis. However, Newton-Leibniz connect antiderivative and integration by\u00a0giving a formula:\u222ba<\/sup>b<\/sub>f (x) dx = F(b)\u2212F(a). In some cases, the integral of function f(x) on closed interval [a,b] can be calculated from the difference of its\u00a0bounds\u2019\u00a0antiderivative[(F(a)-F(b)]. When we do the calculation of antiderivative, we come up with a formula with an inconstant\u00a0instead a definite value, which is the outcome of integral.\u00a0A continues function must have its antiderivative. A function with first discontinuous points does not have its antiderivative.<\/p>\n Antiderivative and integral are two different things: if on interval[a,b], F\u2019(x)=f(x), we can say F(x) is one of antiderivatives of f(x) on this interval. Based on this case, if F(x) is one of antiderivatives of f(x), F(x)+C(C is a random constant) is antiderivative of f(x). Then if f(x) is able to be integrated on [a,b], it may not have antiderivative. If f(x) is continuous on [a,b], f(x) constantly has its antiderivative G(x) and G(x) is its upper limit function: F(x)=\u222bx<\/sup>a<\/sub>f(t)dt+C<\/p>\n In fact, the antiderivative equals indefinite integral. A continuous function can have infinite antiderivatives, but can have only 1 definite value of integral(interval must be given).<\/p>\n","protected":false},"excerpt":{"rendered":" The Difference and Connection between Antiderivative and Integral The antiderivative is the inverse process of the derivative.The\u00a0integral is to calculate the area closed by the graph of a function and x(or y) axis. However, Newton-Leibniz connect antiderivative and integration by\u00a0giving a formula:\u222babf (x) dx = F(b)\u2212F(a). In some cases, the integral of function f(x) on […]<\/p>\n","protected":false},"author":44338,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-19","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/posts\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/users\/44338"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/posts\/19\/revisions"}],"predecessor-version":[{"id":21,"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/posts\/19\/revisions\/21"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/media?parent=19"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/categories?post=19"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/rhein\/wp-json\/wp\/v2\/tags?post=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}