{"id":20674,"date":"2023-11-19T12:04:26","date_gmt":"2023-11-19T05:04:26","guid":{"rendered":"https:\/\/hotelier.id\/studi\/?p=20674"},"modified":"2023-11-19T12:04:26","modified_gmt":"2023-11-19T05:04:26","slug":"rumus-integral-parsial","status":"publish","type":"post","link":"https:\/\/hotelier.id\/studi\/rumus-integral-parsial\/","title":{"rendered":"Rumus Integral Parsial Lengkap dengan Soal dan Pembahasan"},"content":{"rendered":"\n<p>Dalam ilmu matematika, materi integral dibagi menjadi dua berdasarkan tekniknya, yaitu integral parsial dan integral substitusi. Kedua integral ini hampir sama, perbedaannya yakni pada cara dan komponen yang diintegrasikan. Pada artikel ini akan fokus membahas rumus integral parsial yang lengkap dengan soal dan pembahasannya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Integral Parsial<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"340\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/1.-Rumus-Integral-Parsial.png\" alt=\"Contoh persamaan integral \" class=\"wp-image-20678\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/1.-Rumus-Integral-Parsial.png 512w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/1.-Rumus-Integral-Parsial-300x199.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption class=\"wp-element-caption\">Contoh persamaan integral | Sumber: pexel.com<\/figcaption><\/figure><\/div>\n\n\n<p>Sebelum menguraikan rumus integral parsial, sebaiknya&nbsp; ketahui dulu pengertiannya. Adapun integral parsial merupakan suatu teknik pengintegralan dengan cara parsial, yang mana dengan pemisahan, karena komponen yang diintegrasikan memuat variabel yang sama, tetapi berbeda fungsinya.&nbsp;<\/p>\n\n\n\n<p>Biasanya, jenis integral ini orang gunakan untuk menyelesaikan suatu persamaan yang kompleks. Selain itu, cara ini juga biasanya digunakan ketika cara substitusi tidak berhasil dalam menyelesaikan permasalahan matematika.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Rumus Integral Parsial<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"341\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/2.-Rumus-Integral-Parsial.png\" alt=\"Contoh Penyelesaian soal dengan rumus integral \" class=\"wp-image-20681\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/2.-Rumus-Integral-Parsial.png 512w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/2.-Rumus-Integral-Parsial-300x200.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption class=\"wp-element-caption\">Contoh Penyelesaian soal dengan rumus integral | Sumber: Pexels.com<\/figcaption><\/figure><\/div>\n\n\n<p>Pada dasarnya, bentuk rumus umum dari integral parsial sebagai berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"51\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112314339.png\" alt=\"\" class=\"wp-image-20684\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112314339.png 307w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112314339-300x50.png 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/figure>\n\n\n\n<p>Adapun rumus tersebut diperoleh dari persamaan berikut ini:<\/p>\n\n\n\n<p>u = f(x) jadi du = f(x) dx<\/p>\n\n\n\n<p>dv = g(x) dx dari v = g(x) dx<\/p>\n\n\n\n<p>Namun, jika f(x) berupa polinom derajat n \u2265 1, n \u2208 asli, maka bentuk formula tersebut bisa disederhanakan seperti skema berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/-8fA4id2tllt5v3rIa2S1ToMu4qDz5QpnC5RF7pHHWSojxTntN7yXgp8A2P-pO7KVK5_f84JKZD7kRf1PMH_t7Awca8WniI0reVtlsIGxWCaEXsRkSnInd18C71T7ule4FVVOlFtsw6P-JnJBt5UU-g\" alt=\"\" \/><\/figure>\n\n\n\n<p>Adapun tabel tersebut maksudnya, yaitu kolom fungsi f(x) di sebelah kiri adalah fungsi yang diturunkan hingga turunannya bernilai 0. Sedangkan jika kolom fungsi g(x) atau yang sebelah kanan harus diintegralkan sampai kolom sebelah kiri bernilai 0.&nbsp;<\/p>\n\n\n\n<p>Selain itu, tanda fungsi tersebut selalu berselang-seling, yaitu dari positif (+) menjadi negatif (-) dan seterusnya. Untuk itulah, lebih lanjut rumus integral tersebut bisa kamu tulis juga sebagai berikut:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"359\" height=\"50\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112343419.png\" alt=\"\" class=\"wp-image-20685\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112343419.png 359w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112343419-300x42.png 300w\" sizes=\"auto, (max-width: 359px) 100vw, 359px\" \/><\/figure>\n\n\n\n<p>Tidak hanya itu, rumus integral parsial juga bisa dibagi menjadi dua tipe, yaitu integral tak tentu dengan integral tentu. Adapun rumus untuk integral parsial tak tentu sebagai berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"50\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112409139.png\" alt=\"\" class=\"wp-image-20686\" \/><\/figure>\n\n\n\n<p>Sedangkan rumus untuk integral parsial tentu, yaitu:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"387\" height=\"154\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112432095.png\" alt=\"\" class=\"wp-image-20687\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112432095.png 387w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_112432095-300x119.png 300w\" sizes=\"auto, (max-width: 387px) 100vw, 387px\" \/><\/figure>\n\n\n\n<p><strong>Baca Juga : <a href=\"https:\/\/hotelier.id\/studi\/integer-adalah\" target=\"_blank\" rel=\"noreferrer noopener\">Integer Adalah: Pengertian, Ukuran, dan Contoh Penggunaannya<\/a><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Contoh Soal Integral Parsial dan Pembahasan<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"341\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/3.-Contoh-Soal-Integral-Parsial-dan-Pembahasan.png\" alt=\"Seseorang sedang mengerjakan soal matematika\" class=\"wp-image-20680\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/3.-Contoh-Soal-Integral-Parsial-dan-Pembahasan.png 512w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/3.-Contoh-Soal-Integral-Parsial-dan-Pembahasan-300x200.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption class=\"wp-element-caption\">Seseorang sedang mengerjakan soal matematika | Sumber: Pexels.com<\/figcaption><\/figure><\/div>\n\n\n<p>Untuk lebih jelasnya mengenai penjelasan rumus integral parsial tersebut, berikut ini contoh soalnya lengkap dengan pembahasan:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Soal 1<\/h3>\n\n\n\n<p>Berapakan hasil integral dari \u0283 x2 cos x dx?&nbsp;<\/p>\n\n\n\n<p>Pembahasan:<\/p>\n\n\n\n<p>Pertama-tama kita misalkan bahwa:<\/p>\n\n\n\n<p>\u0283 x cos x dx = \u0283 u dv<\/p>\n\n\n\n<p>Maka, kamu bisa mengetahui bahwa:<\/p>\n\n\n\n<p>u = x, jadi diperoleh du = 1 dx<\/p>\n\n\n\n<p>dv = cos x dx, jadi diperoleh v = sin x<\/p>\n\n\n\n<p>Selanjutnya, distribusikan 4 variabel tersebut, sehingga diperoleh penyelesaian sebagai berikut:<\/p>\n\n\n\n<p>\u0283 x cos x dx = \u0283 u dv<\/p>\n\n\n\n<p>\u0283 x cos x dx = uv \u2013 \u0283 v du<\/p>\n\n\n\n<p>Lalu,<\/p>\n\n\n\n<p>\u0283 x cos x dx = x (sin x) \u2013 \u0283 sin x (1 dx)<\/p>\n\n\n\n<p>\u0283 x cos x dx = x sin x \u2013 \u0283 sin x dx<\/p>\n\n\n\n<p>Sederhanakan lagi menjadi,<\/p>\n\n\n\n<p>\u0283 x cos x dx = x sin x \u2013 (-cos x)<\/p>\n\n\n\n<p>\u0283 x cos x dx = x sin x + cos x<\/p>\n\n\n\n<p>Jadi hasil akhirnya adalah x sin x + cos x.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Soal 2<\/h3>\n\n\n\n<p>Tentukan, berapakah hasil integral dari persamaan berikut ini:<\/p>\n\n\n\n<p>\u0283 Inxdx<\/p>\n\n\n\n<p>Pembahasan:<\/p>\n\n\n\n<p>Adapun bentuk soal tersebut bisa kamu selesaikan dengan metode dasar, karena tidak memiliki polinom derajat dari bilangan aslinya. Selanjutnya, kamu bisa misalkan rumusnya untuk mulai menyelesaikan soal tersebut.&nbsp;<\/p>\n\n\n\n<p>Misal:<\/p>\n\n\n\n<p>u = Inx, maka du = 1\/x dx<\/p>\n\n\n\n<p>dv = dx, maka v = x<\/p>\n\n\n\n<p>Selanjutnya, kamu bisa mulai memasukkannya ke dalam persamaan seperti berikut:<\/p>\n\n\n\n<p>\u0283 Inx dx = u v &#8211; \u0283 v du<\/p>\n\n\n\n<p>\u0283 Inx dx = (Inx (x) &#8211; \u0283 x (1\/x dx)<\/p>\n\n\n\n<p>Kemudian, sederhanakan menjadi:<\/p>\n\n\n\n<p>\u0283 Inx dx = x Inx &#8211; \u0283 dx<\/p>\n\n\n\n<p>\u0283 Inx dx = x Inx \u2013 x + c<\/p>\n\n\n\n<p>Maka, hasil integral dari Inx dx adalah x Inx \u2013 x + c.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Soal 3<\/h3>\n\n\n\n<p>Tentukan berapakah integral dari:<\/p>\n\n\n\n<p>\u0283 2x (5x + 1)<sup>6<\/sup> dx<\/p>\n\n\n\n<p>Pembahasan:&nbsp;&nbsp;<\/p>\n\n\n\n<p>Pertama, misalkan 2x = u, jadi 2 dx = du<\/p>\n\n\n\n<p>Kemudian, misalkan juga dv = (5x + 1)<sup>6<\/sup> dx,&nbsp;<\/p>\n\n\n\n<p>maka v = (1\/5) (1\/7) (5x + 1)<sup>7<\/sup> = 1\/35 (5x + 1)<sup>7<\/sup><\/p>\n\n\n\n<p>Jadi, penyelesaian untuk soal tersebut sebagai berikut:<\/p>\n\n\n\n<p>\u0283 2x (5x + 1)6 dx = 2x (1\/35) (5x + 1)2 &#8211; 1\/35 (5x + 1)7 2 dx<\/p>\n\n\n\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 2x\/35 (5x + 1)<sup>7<\/sup> &#8211; 2\/35 (1\/5) (1\/8) (5x + 1)<sup>8<\/sup> + c<\/p>\n\n\n\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 2x\/35 (5x + 1)<sup>7<\/sup> &#8211; 1\/700 (5x + 1)<sup>8<\/sup> + c<\/p>\n\n\n\n<p>Maka, hasil integral dari \u0283 2x (5x + 1)<sup>6<\/sup> dx adalah 2x\/35 (5x + 1)<sup>7<\/sup> &#8211; 1\/700 (5x + 1)<sup>8<\/sup> + c.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Soal 4<\/h3>\n\n\n\n<p>Berapakah hasil integral dari :<\/p>\n\n\n\n<p>\u0283 x (x + 4)<sup>5<\/sup> dx\u00a0<\/p>\n\n\n\n<p>Pembahasan:<\/p>\n\n\n\n<p>Hal yang pertama untuk menyelesaikan soal tersebut adalah dengan membuat permisalan sebagai berikut:<\/p>\n\n\n\n<p>u = x, maka du = dx<\/p>\n\n\n\n<p>dv = (x + 4)<sup>5<\/sup> dx, maka v = 1\/6 (x + 4)<sup>6<\/sup><\/p>\n\n\n\n<p>Dengan menggunakan rumus integral parsial, maka penyelesaiannya sebagai berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"505\" height=\"352\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121247278.png\" alt=\"\" class=\"wp-image-20690\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121247278.png 505w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121247278-300x209.png 300w\" sizes=\"auto, (max-width: 505px) 100vw, 505px\" \/><\/figure>\n\n\n\n<p>Jadi hasil integral dari <\/p>\n\n\n\n<p>\u0283 x (x + 4)<sup>5<\/sup> dx\u00a0 adalah 1\/21 (3x &#8211; 2)(x + 4)<sup>6<\/sup> + c.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Soal 5<\/h3>\n\n\n\n<p>Berapakah hasil dari <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"145\" height=\"44\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121652582.png\" alt=\"\" class=\"wp-image-20694\" \/><\/figure>\n\n\n\n<p>Pembahasan:<\/p>\n\n\n\n<p>Untuk menyelesaikan soal tersebut, kamu bisa misalkan terlebih dahulu:<\/p>\n\n\n\n<p>u = x, maka du = dx<\/p>\n\n\n\n<p>dv = (x + 4)<sup>5<\/sup> dx, maka v = 1\/6\u00a0 (x + 4)<sup>6<\/sup><\/p>\n\n\n\n<p>Selanjutnya, dengan menggunakan rumus integral parsial, kamu bisa menyelesaikannya seperti berikut:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"490\" height=\"331\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121825140.png\" alt=\"\" class=\"wp-image-20695\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121825140.png 490w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121825140-300x203.png 300w\" sizes=\"auto, (max-width: 490px) 100vw, 490px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"598\" height=\"38\" src=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121849844.png\" alt=\"\" class=\"wp-image-20696\" srcset=\"https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121849844.png 598w, https:\/\/hotelier.id\/studi\/wp-content\/uploads\/2023\/10\/image_2023-10-09_121849844-300x19.png 300w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Sudah Tahu Rumus Integral Parsial?&nbsp;<\/h2>\n\n\n\n<p>Untuk menghitung integral parsial memang tidak semudah yang dibayangkan. Mengingat rumusnya yang cukup banyak dan sangat rumit, sehingga memerlukan tenaga ekstra untuk memikirkan cara menyelesaikan soalnya.&nbsp;<\/p>\n\n\n\n<p>Namun dengan berlatih secara rutin dan terstruktur, maka tidak ada yang tidak mungkin untuk bisa menyelesaikan soal integral ini. Kamu bisa berlatih menggunakan beberapa soal di atas atau mencari soal yang lain dan berlandaskan pada pembahasan tersebut. Semoga membantu!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Integral parsial adalah suatu teknik pengintegralan dengan cara parsial. Yuk, ketahui rumus integral parsial dengan soal dan pembahasannya ini!<\/p>\n","protected":false},"author":2,"featured_media":20677,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-20674","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","infinite-scroll-item","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rumus Integral Parsial Lengkap dengan Soal dan Pembahasan - Hotelier Studi<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hotelier.id\/studi\/rumus-integral-parsial\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rumus Integral Parsial Lengkap dengan Soal dan Pembahasan - Hotelier Studi\" \/>\n<meta property=\"og:description\" content=\"Integral parsial adalah suatu teknik pengintegralan dengan cara parsial. 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