{"id":996,"date":"2024-10-28T12:20:05","date_gmt":"2024-10-28T04:20:05","guid":{"rendered":"https:\/\/www.math.ntnu.edu.tw\/merc\/?page_id=996"},"modified":"2025-10-23T11:20:32","modified_gmt":"2025-10-23T03:20:32","slug":"trapezoidalrule","status":"publish","type":"page","link":"https:\/\/www.math.ntnu.edu.tw\/merc\/animated_math\/trapezoidalrule\/","title":{"rendered":"\u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"996\" class=\"elementor elementor-996\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3406f55b e-flex e-con-boxed e-con e-parent\" data-id=\"3406f55b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-41b32277 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"41b32277\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;bounceIn&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u821e\u52d5\u6578\u5b78<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3fe87720 e-flex e-con-boxed e-con e-parent\" data-id=\"3fe87720\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-62699e13 elementor-widget elementor-widget-heading\" data-id=\"62699e13\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2b75fa47 e-flex e-con-boxed e-con e-parent\" data-id=\"2b75fa47\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-280598f elementor-widget elementor-widget-video\" data-id=\"280598f\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247.mov\" autoplay=\"\" loop=\"\" controls=\"\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6682f913 e-flex e-con-boxed e-con e-parent\" data-id=\"6682f913\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-23d93f7 elementor-widget elementor-widget-text-editor\" data-id=\"23d93f7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h4>\u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247<\/h4>\n<div>\u68af\u5f62\u6cd5\u5247\u662f\u4e00\u7a2e\u900f\u904e\u5c07\u66f2\u7dda\u4e0b\u65b9\u7684\u9762\u7a4d\u5283\u5206\u70ba\u68af\u5f62\u4f86\u8fd1\u4f3c\u51fd\u6578\u7a4d\u5206\u7684\u65b9\u6cd5\u3002<\/div>\n<div>Area=$\\frac{1}{2}(a+h)h$<\/div>\n<div>$f(x)=x^3+2x^2+3x+4$<\/div>\n<div>$\\displaystyle \\int_a^b f(x)dx \\approx \\sum_{i=0}^{n-1} \\frac{1}{2}\\left( f(x_i)+f(x_{i+1}) \\right) (x_{i+1}-x_i)$<\/div>\n<div>Actual integral value=297.08<\/div>\n<div>n=6\nSum of the areas of trapezoids=305.00\nERROR=7.92<\/div>\n<div>n=11\nSum of the areas of trapezoids=299.06\nERROR=1.98<\/div>\n<div>n=101\nSum of the areas of trapezoids=297.10\nERROR=0.02<\/div>\n<div>As the number of trapezoids increases, the approximation of the integral becomes more accurate.<\/div>\n<div style=\"margin-top: 20px;\"><a style=\"font-size: 32; color: red;\" href=\"https:\/\/www.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247\u5b78\u7fd2\u55ae.pdf\" target=\"_blank\" rel=\"noopener\">\u5b78\u7fd2\u55ae\uff1a\u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247\u5b78\u7fd2\u55ae<\/a><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-353dd0da e-flex e-con-boxed e-con e-parent\" data-id=\"353dd0da\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1e2736ab elementor-widget elementor-widget-text-editor\" data-id=\"1e2736ab\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<hr style=\"margin-bottom: 10px;\" \/>\n<p style=\"color: #306f7f;\">\u88fd\u4f5c\u4eba\uff1a\u6797\u5b87\u661f<br>\u5b78\u7fd2\u55ae\uff1a\u8607\u9e97\u654f<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u821e\u52d5\u6578\u5b78 \u6578\u503c\u7a4d\u5206\uff1a \u68af\u5f62\u6cd5\u5247 https:\/\/cantor.math.ntnu.edu.tw\/worksho [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":193,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_post_layout":"full-width","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-996","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/996","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/comments?post=996"}],"version-history":[{"count":20,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/996\/revisions"}],"predecessor-version":[{"id":1512,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/996\/revisions\/1512"}],"up":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/193"}],"wp:attachment":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/media?parent=996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}