{"id":1618,"date":"2020-04-04T10:20:37","date_gmt":"2020-04-04T10:20:37","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1618"},"modified":"2020-04-05T08:22:10","modified_gmt":"2020-04-05T08:22:10","slug":"ibdp-past-year-exam-questions-introduction-to-integration","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/introduction-to-integration\/ibdp-past-year-exam-questions-introduction-to-integration\/","title":{"rendered":"IBDP Past Year Exam Questions &#8211; Introduction to Integration"},"content":{"rendered":"<p><strong>1.[M97\/P1]<\/strong><\/p>\r\n<p>Find the indefinite integral\u00a0 \u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8747;<\/mo><msup><mfenced><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&#8211;<\/mo><mn>1<\/mn><\/mrow><\/mfenced><mn>3<\/mn><\/msup><mi>x<\/mi><mo>&#160;<\/mo><mi>d<\/mi><mi>x<\/mi><\/math>\r\n .<\/p>\r\n<p><strong>2.[M97\/P1]<\/strong><\/p>\r\n<p>Using the substitution\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>u<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/math>\r\n , or otherwise, find the integral<\/p>\r\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8747;<\/mo><mi>x<\/mi><msqrt><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/msqrt><mo>&#160;<\/mo><mi>d<\/mi><mi>x<\/mi><\/math>\r\n.<\/p>\r\n<p><strong>3. [M15\/P1\/TZ1]<\/strong><\/p>\r\n<p>(a)\u00a0 Find\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8747;<\/mo><mfenced><mrow><mn>1<\/mn><mo>+<\/mo><msup><mi>tan<\/mi><mn>2<\/mn><\/msup><mi>x<\/mi><\/mrow><\/mfenced><mo>&#160;<\/mo><mi>d<\/mi><mi>x<\/mi><\/math>\r\n.\u00a0 \u00a0 [2 marks]<\/p>\r\n<p>(b)\u00a0 \u00a0Find\u00a0\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&#8747;<\/mo><msup><mi>sin<\/mi><mn>2<\/mn><\/msup><mi>x<\/mi><mo>&#160;<\/mo><mi>d<\/mi><mi>x<\/mi><\/math>\r\n.\u00a0 \u00a0 \u00a0 \u00a0 [3 marks]<\/p>\r\n<div id=\"link3-link-1618\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 1618, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-1618\">Solution<\/span><\/a><\/div><div id=\"link3-content-1618\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1636\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-31.jpg\" alt=\"\" width=\"758\" height=\"168\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-31.jpg 758w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-31-300x66.jpg 300w\" sizes=\"auto, (max-width: 758px) 100vw, 758px\" \/><\/p>\r\n<p>\u00a0<\/div><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1.[M97\/P1] Find the indefinite integral\u00a0 \u00a0 &#8747;x2&#8211;13x&#160;dx . 2.[M97\/P1] Using the substitution\u00a0 u=12x+1 , or otherwise, find the integral \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8747;x12x+1&#160;dx . 3. [M15\/P1\/TZ1] (a)\u00a0 Find\u00a0 &#8747;1+tan2x&#160;dx .\u00a0 \u00a0 [2 marks] (b)\u00a0 \u00a0Find\u00a0\u00a0 &#8747;sin2x&#160;dx .\u00a0 \u00a0 \u00a0 \u00a0 [3 marks]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1618","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-introduction-to-integration","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1618","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1618"}],"version-history":[{"count":5,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1618\/revisions"}],"predecessor-version":[{"id":1637,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1618\/revisions\/1637"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}