{"id":362828,"date":"2023-01-07T09:14:20","date_gmt":"2023-01-07T03:44:20","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/i%e2%88%ab%cf%80-4%cf%80-3%e2%80%8a8sin%e2%81%a1x%e2%88%92sin%e2%81%a12xxdx-then\/"},"modified":"2025-06-26T13:11:16","modified_gmt":"2025-06-26T07:41:16","slug":"i%e2%88%ab%cf%80-4%cf%80-3%e2%80%8a8sin%e2%81%a1x%e2%88%92sin%e2%81%a12xxdx-then","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/","title":{"rendered":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then","custom_permalink":"question\/mathematics\/i438sinxsin2xxdx-then\/"},"categories":[],"acf":{"question":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">I<\/mi><mo>=<\/mo><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mo>\u200a<\/mo><mfenced separators=\"|\"><mfrac><mrow><mn>8<\/mn><mi>sin<\/mi><mo>\u2061<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>\u2212<\/mo><mi>sin<\/mi><mo>\u2061<\/mo><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><\/mrow><mi mathvariant=\"normal\">x<\/mi><\/mfrac><\/mfenced><mi>dx<\/mi><\/math>. Then<\/p>","options":[{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><mn>2<\/mn><\/mfrac><mo>&lt;<\/mo><mi mathvariant=\"normal\">I<\/mi><mo>&lt;<\/mo><mfrac><mrow><mn>3<\/mn><mi mathvariant=\"normal\">\u03c0<\/mi><\/mrow><mn>4<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><mn>5<\/mn><\/mfrac><mo>&lt;<\/mo><mi mathvariant=\"normal\">I<\/mi><mo>&lt;<\/mo><mfrac><mrow><mn>5<\/mn><mi mathvariant=\"normal\">\u03c0<\/mi><\/mrow><mn>12<\/mn><\/mfrac><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mn>5<\/mn><mi mathvariant=\"normal\">\u03c0<\/mi><\/mrow><mn>12<\/mn><\/mfrac><mo>&lt;<\/mo><mi mathvariant=\"normal\">I<\/mi><mo>&lt;<\/mo><mfrac><msqrt><mn>2<\/mn><\/msqrt><mn>3<\/mn><\/mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><\/math><\/p>","correct":true},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mn>3<\/mn><mi mathvariant=\"normal\">\u03c0<\/mi><\/mrow><mn>4<\/mn><\/mfrac><mo>&lt;<\/mo><mi mathvariant=\"normal\">I<\/mi><mo>&lt;<\/mo><mi mathvariant=\"normal\">\u03c0<\/mi><\/math><\/p>","correct":false}],"solution":"<p>Consider<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><mi mathvariant=\"normal\">f<\/mi><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>=<\/mo><mn>8<\/mn><mi>sinx<\/mi><mo>\u2212<\/mo><mi>sin<\/mi><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><\/mtd><\/mtr><mtr><mtd><msup><mi mathvariant=\"normal\">f<\/mi><mo>'<\/mo><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>=<\/mo><mn>8<\/mn><mi>cosx<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mi>cos<\/mi><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><\/mtd><\/mtr><mtr><mtd><msup><mi mathvariant=\"normal\">f<\/mi><mo>''<\/mo><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>8<\/mn><mi>sinx<\/mi><mo>+<\/mo><mn>4<\/mn><mi>sin<\/mi><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><\/mtd><\/mtr><mtr><mtd><mo>=<\/mo><mo>\u2212<\/mo><mn>8<\/mn><mi>sinx<\/mi><mo>(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>cosx<\/mi><mo>)<\/mo><\/mtd><\/mtr><mtr><mtd><mo>\u2234<\/mo><msup><mi mathvariant=\"normal\">f<\/mi><mo>\u2032\u2032<\/mo><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>&lt;<\/mo><mn>0<\/mn><mo>,<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>\u2208<\/mo><mfenced separators=\"|\"><mrow><mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><mn>4<\/mn><\/mfrac><mo>,<\/mo><mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><mn>3<\/mn><\/mfrac><\/mrow><\/mfenced><\/mtd><\/mtr><mtr><mtd><mo>\u2234<\/mo><msup><mi mathvariant=\"normal\">f<\/mi><mrow><mo>&nbsp;<\/mo><mi mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mtext>&nbsp;is&nbsp;<\/mtext><mo stretchy=\"false\">\u2193<\/mo><mtext>&nbsp;function&nbsp;<\/mtext><\/mtd><\/mtr><mtr><mtd><msup><mi mathvariant=\"normal\">f<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mfenced separators=\"|\"><mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><mn>3<\/mn><\/mfrac><\/mfenced><mo>&lt;<\/mo><msup><mi mathvariant=\"normal\">f<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>&lt;<\/mo><msup><mi mathvariant=\"normal\">f<\/mi><mi mathvariant=\"normal\">\u2032<\/mi><\/msup><mfenced separators=\"|\"><mfrac><mi mathvariant=\"normal\">\u03c0<\/mi><mn>4<\/mn><\/mfrac><\/mfenced><\/mtd><\/mtr><mtr><mtd><mn>5<\/mn><mo>&lt;<\/mo><msup><mi mathvariant=\"normal\">f<\/mi><mrow><mo>&nbsp;<\/mo><mi mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>&lt;<\/mo><mfrac><mn>8<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><mn>5<\/mn><mo>&lt;<\/mo><msup><mi mathvariant=\"normal\">f<\/mi><mrow><mo>&nbsp;<\/mo><mi mathvariant=\"normal\">\u2032<\/mi><\/mrow><\/msup><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>&lt;<\/mo><mn>4<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mtd><\/mtr><mtr><mtd><mn>5<\/mn><mi mathvariant=\"normal\">x<\/mi><mo>&lt;<\/mo><mi mathvariant=\"normal\">f<\/mi><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><mo>&lt;<\/mo><mn>4<\/mn><msqrt><mn>2<\/mn><\/msqrt><mi mathvariant=\"normal\">x<\/mi><\/mtd><\/mtr><mtr><mtd><mn>5<\/mn><mo>&lt;<\/mo><mfrac><mrow><mi mathvariant=\"normal\">f<\/mi><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><\/mrow><mi mathvariant=\"normal\">x<\/mi><\/mfrac><mo>&lt;<\/mo><mn>4<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mtd><\/mtr><mtr><mtd><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mo>\u200a<\/mo><mn>5<\/mn><mo>&lt;<\/mo><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mfrac><mrow><mi mathvariant=\"normal\">f<\/mi><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>)<\/mo><\/mrow><mi mathvariant=\"normal\">x<\/mi><\/mfrac><mo>&lt;<\/mo><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mo>\u200a<\/mo><mn>4<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mtd><\/mtr><mtr><mtd><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mo>\u200a<\/mo><mn>5<\/mn><mo>&lt;<\/mo><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mfrac><mrow><mn>8<\/mn><mi>sinx<\/mi><mo>\u2212<\/mo><mi>sin<\/mi><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><\/mrow><mi mathvariant=\"normal\">x<\/mi><\/mfrac><mo>&lt;<\/mo><msubsup><mo>\u222b<\/mo><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>4<\/mn><\/mrow><mrow><mi mathvariant=\"normal\">\u03c0<\/mi><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msubsup><mo>\u200a<\/mo><mn>4<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mtd><\/mtr><mtr><mtd><mfrac><mrow><mn>5<\/mn><mi mathvariant=\"normal\">\u03c0<\/mi><\/mrow><mn>12<\/mn><\/mfrac><mo>&lt;<\/mo><mi mathvariant=\"normal\">I<\/mi><mo>&lt;<\/mo><mfrac><mrow><msqrt><mn>2<\/mn><\/msqrt><mi mathvariant=\"normal\">\u03c0<\/mi><\/mrow><mn>3<\/mn><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-26T07:41:16+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then - Infinity Learn by Sri Chaitanya","description":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/","og_locale":"en_US","og_type":"article","og_title":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then - Infinity Learn by Sri Chaitanya","og_description":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then","og_url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-26T07:41:16+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/","name":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2023-01-07T03:44:20+00:00","dateModified":"2025-06-26T07:41:16+00:00","description":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/i438sinxsin2xxdx-then\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"I=\u222b\u03c0\/4\u03c0\/3\u200a8sin\u2061x\u2212sin\u20612xxdx. Then"}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/362828"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=362828"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=362828"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}