{"id":26864,"date":"2024-10-22T11:45:49","date_gmt":"2024-10-22T06:15:49","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=26864"},"modified":"2024-10-23T10:06:24","modified_gmt":"2024-10-23T04:36:24","slug":"samacheer-kalvi-11th-maths-guide-chapter-11-ex-11-7","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-11th-maths-guide-chapter-11-ex-11-7\/","title":{"rendered":"Samacheer Kalvi 11th Maths Guide Chapter 11 Integral Calculus Ex 11.7"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide<\/a> Pdf Chapter 11 Integral Calculus Ex 11.7 Text Book Back Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.7<\/h2>\n

Integrate the following with respect to x:<\/p>\n

Question 1.
\n(i) 9x e3x<\/sup>
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(ii) x sin 3x
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iii) 25 x e-5x<\/sup>
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iv) x sec x tan x
\nAnswer:
\n\u222b x sec x tan x dx
\nu = x, u’ = 1 , u” = 0
\ndv = sec x tan x dx , v = \u222b sec x tan x dx = sec x
\nv1<\/sub> = \u222b v dx = \u222b sec x dx = log |sec x + tan x|
\nv2<\/sub> = \u222b v1<\/sub> dx = \u222b log |sec x + tan x| dx
\n\u222b u dv = uv – u’ v1<\/sub> + u” v2<\/sub> – u”’ v3<\/sub> + ………….
\n\u222bx sec x tan x dx = x sec x – 1 \u00d7 log |sec x + tan x| + 0 \u00d7 \u222b log |x sec x tan x| + c
\n\u222bx sec x tan x dx = x sec x – log |sec x + tan x| + c<\/p>\n

Question 2.
\n(i) x log x
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(ii) 27 x2<\/sup> e3x<\/sup>
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iii) x2<\/sup> cos x
\nAnswer:
\n\"Samacheer<\/p>\n

(iv) x3<\/sup> sin x
\nAnswer:
\n\u222b x3<\/sup> sin x
\nu = x3<\/sup>, u’ = 3x2<\/sup>, u” = 6x , u”’ = 6 , u’v<\/sup> = 0
\ndv = sin x dx \u21d2 v = \u222b sin x dx = – cosx
\nv1<\/sub> = \u222bv dx = \u222b- cos x dx = – \u222b cos x dx = – sin x
\nv2<\/sub> = \u222b v1<\/sub> dx = \u222b – sin x dx = – \u222b sin x dx = – (- cos x) = cos x
\nv3<\/sub> = \u222b v2<\/sub> dx = \u222b cos x dx = sin x
\nv4<\/sub> = \u222b v3<\/sub> dx = \u222b sin x dx = – cos x
\n\u222b u dv = uv – u’ v1<\/sub> + u” v2<\/sub> – u”’ v3<\/sub> + u’v<\/sup>v4<\/sub> – ………..
\n\u222bx3<\/sup> sin x dx = x3<\/sup> (- cos x) – 3x2<\/sup> (- sin x) + 6x (cos x) – 6 sin x + 0 (- cos x) + c
\n= -x3<\/sup> cos x + 3x2<\/sup> sin x + 6x cos x – 6 sin x + c<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\n(i) \"Samacheer
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(ii) x5<\/sup> ex2<\/sup><\/sup>
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iii) \"Samacheer
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iv) \"Samacheer
\nAnswer:
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide Pdf Chapter 11 Integral Calculus Ex 11.7 Text Book Back Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.7 Integrate the following with respect to x: Question 1. (i) 9x e3x Answer: (ii) x sin 3x Answer: (iii) 25 …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-26864","post","type-post","status-publish","format-standard","hentry","category-class-11"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/26864"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=26864"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/26864\/revisions"}],"predecessor-version":[{"id":41391,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/26864\/revisions\/41391"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=26864"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=26864"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=26864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}