{"id":39889,"date":"2019-04-24T05:21:27","date_gmt":"2019-04-24T05:21:27","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=39889"},"modified":"2020-12-08T12:22:28","modified_gmt":"2020-12-08T06:52:28","slug":"plus-two-maths-chapter-wise-previous-questions-chapter-7","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-7\/","title":{"rendered":"Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals"},"content":{"rendered":"

Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers<\/a>. Here we have given Plus Two Maths Chapter Wise Previous Chapter 7 Integrals.<\/p>\n

Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 7 Integrals<\/h2>\n

Plus Two Maths Application of Derivatives 3 Marks Important Questions<\/h3>\n

Question 1.
\nFind the following integrals. (May -2011)<\/span>
\n\\(\\begin{array}{l}
\n\\text { (i) } \\int x^{2} e^{2 x} d x \\\\
\n\\text { (ii) } \\int e^{x} \\sin x d x
\n\\end{array}\\)
\nAnswer:
\n\"Plus<\/p>\n

Question 2.
\n(i) \\(\\int e^{x} \\sec x(1+\\tan x) d x=\\ldots \\ldots\\)
\n(a) ex cosx + c (b) ex sec x + c
\n(C) ex tanx + c (d) ex sin x + c
\n(ii) Find \\(\\int \\sin 2 x \\cos 3 x d x\\) (March – 2014)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 3.
\nFind the following integrals.
\n(i) \\(\\begin{array}{l}
\n\\text { (i) } \\int \\frac{1}{(x+1)(x+2)} d x \\\\
\n\\text { (ii) } \\int \\frac{2 x-1}{(x-1)(x+2)^{2}} d x
\n\\end{array}\\) (March – 2014)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Plus Two Maths Application of Derivatives 4 Marks Important Questions<\/h3>\n

Question 1.
\nConsider the integral \\(I=\\int_{0}^{\\pi} \\frac{x \\sin x}{1+\\cos ^{2} x} d x\\)
\n(i) Express \\(I=\\frac{\\pi}{2} \\int_{0}^{\\pi} \\frac{\\sin x}{1+\\cos ^{2} x} d x\\)
\n(ii) Show that \\(I=\\frac{\\pi^{2}}{4}\\) (March – 2012)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 2.
\n(i) Evaluate: \\(\\int_{2}^{3} \\frac{x}{x^{2}+1} d x\\)
\n(ii) Evaluate: \\(\\int_{0}^{\\pi} \\frac{x}{1+\\sin x} d x\\) (March – 2014)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 3.
\n(a) What is the value of \\(\\int_{0}^{1} x(1-x)^{9} d x\\) If the
\n\\(\\begin{array}{llll}
\n\\text { (i) } \\frac{1}{10} & \\text { (ii) } \\frac{1}{11} & \\text { (iii) } \\frac{1}{90} & \\text { (iv) } \\frac{1}{110}
\n\\end{array}\\)
\n(b) Find \\(\\int_{0}^{1}(2 x+3) d x\\) of a sum. (March – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 4.
\nEvaluate \\(\\int_{0}^{x} \\log (1+\\cos x) d x\\)
\nAnswer:
\n\"Plus<\/p>\n

Question 5.
\nFind \\(\\int_{0}^{5}(x+1) d x \\text { as limit of a sum. }\\)
\nAnswer:
\n\"Plus<\/p>\n

Question 6.
\nEvaluate \\(\\int_{0}^{4} x^{2} d x\\) as the limit of a sum. (March – 2017)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Plus Two Maths Application of Derivatives 6 Marks Important Questions<\/h3>\n

Question 1.
\n(i) Fill in the blanks; \\(\\int \\frac{1}{x} d x=\\)_____
\n(ii) Evaluate \\(\\int \\frac{5 x+1}{x^{2}-2 x-35} d x\\)
\n(iii) Integrate with respect to x. \\(\\sqrt{x^{2}+4 x+8}\\) (March – 2010)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 2.
\n(i) Evaluate \\(\\int-\\frac{\\cos e c^{2} x}{\\sqrt{\\cot ^{2} x+9}} d x\\)
\n(ii) Evaluate \\(\\int\\left(\\cos ^{-1} x\\right)^{2} d x\\) (May -2010)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 3.
\n(i) Evaluate \\(\\int_{0}^{\\pi} \\frac{x \\sin x}{1+\\cos ^{2} x} d x\\)
\n(ii) Evaluate \\(\\int_{0}^{2} e^{x} d x \\text { as limit of a sum. }\\) (May -2010)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 4.
\n(i) Fill in the blanks \\(\\int \\cot x d x=\\)_____
\n(ii) Evaluate the integrals
\n\\(\\begin{array}{l}
\n\\text { (a) } \\int \\sin 2 x \\cos 4 x d x \\\\
\n\\text { (b) } \\int \\frac{x}{(x+1)(x+2)} d x
\n\\end{array}\\) (March -2011)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 5.
\n(i) Evaluate \\(\\int_{0}^{1} x d x\\) as the limit of a sum.
\n(ii) Evaluate \\(\\int_{0}^{1} x(1-x)^{n} d x\\) (March – 2011)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 6.
\n(i) Evaluate \\(\\int_{1}^{2} \\frac{1}{x(1+\\log x)^{2}} d x\\)
\n(ii) Evaluate \\(\\int_{0}^{3}\\left(2 x^{2}+3\\right) d x\\) as the limit of a sum. (May – 2011)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 7.
\n(i) What is \\(\\int \\frac{1}{9+x^{2}} d x=?\\)
\n(ii) Evaluate the integrals \\(\\int \\frac{1}{1+x+x^{2}+x^{3}} d x\\) (May – 2012)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 8.
\n(i) Evaluate \\(\\int_{0}^{3} f(x) d x\\)
\nwhere \\(f(x)=\\left\\{\\begin{array}{ll}
\nx+3, & 0 \\leq x \\leq 2 \\\\
\n3 x, & 2 \\leq x \\leq 3
\n\\end{array}\\right.\\)<\/p>\n

(ii) Prove that \\(\\int_{0}^{1} \\log \\left(\\frac{x}{1-x}\\right) d x=\\int_{0}^{1} \\log \\left(\\frac{1-x}{x}\\right) d x\\) Find the value of \\(\\int_{0}^{1} \\log \\left(\\frac{x}{1-x}\\right) d x\\) (May – 2012)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 9.
\n(i) Find \\(\\int \\cot x d x=\\ldots \\ldots\\)
\n(ii) Find \\(\\int x \\log x d x\\)
\n(iii) Find \\(\\int \\frac{x-1}{(x-2)(x-3)} d x\\) (March – 2013)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 10.
\nEvaluate
\n\\(\\text { (i) } \\int \\frac{x+3}{\\sqrt{5-4 x-x^{2}}} d x\\)
\n\\(\\text { (ii) } \\int_{\\pi \/ 6}^{\\pi \/ 3} \\frac{d x}{1+\\sqrt{\\tan x}}\\) (May – 2013)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus
\n\"Plus<\/p>\n

Question 11.
\nEvaluate
\n\\(\\begin{array}{l}
\n\\text { (i) } \\int x^{2} \\tan ^{-1} x d x \\\\
\n\\text { (ii) } \\int_{-1}^{2} x^{3}-x d x
\n\\end{array}\\) (May – 2013)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus
\n\"Plus<\/p>\n

Question 12.
\nEvaluate \\(\\int_{0}^{\\pi \/ 4} \\log (1+\\tan x) d x\\) (March – 2013)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 13.
\n(a) The value of \\(\\int_{\\frac{-\\pi}{2}}^{\\frac{\\pi}{2}} \\cos x d x\\) (May – 2014)<\/span>
\n(b) Prove that \\(\\int_{0}^{\\pi} \\frac{x}{a^{2} \\cos ^{2} x+b^{2} \\sin ^{2} x} d x=\\frac{\\pi^{2}}{2 a b}\\)
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 14.
\n(a) \\(\\int \\frac{1}{x^{2}+a^{2}} d x=\\)
\n(b) Find \\(\\int \\frac{1}{9 x^{2}+6 x+5} d x\\)
\n(c) Find \\(\\int \\frac{x}{(x-1)^{2}(x+2)} d x\\) (May – 2014)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 15.
\nIntegrate the following
\n\\(\\begin{array}{l}
\n\\text { (a) } \\frac{x-1}{x+1} \\\\
\n\\text { (b) } \\frac{\\sin x}{\\sin (x-a)} \\\\
\n\\text { (c) } \\frac{1}{\\sqrt{3-2 x-x^{2}}}
\n\\end{array}\\) (March – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 16.
\n(a) Prove that \\(\\int \\cos ^{2} x d x=\\frac{x}{2}+\\frac{\\sin 2 x}{4}+c\\)
\n(b)Find \\(\\int \\frac{1}{\\sqrt{2 x-x^{2}}} d x\\)
\n(c) Find \\(\\int x \\cos x d x\\) (May – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 17.
\nFind the following:
\n\\(\\begin{array}{l}
\n\\text { (i) } \\int \\frac{1}{x\\left(x^{7}+1\\right)} d x \\\\
\n\\text { (ii) } \\int_{1}^{4}|x-2| d x
\n\\end{array}\\)
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 18.
\nFind \\(\\int_{0}^{\\frac{\\pi}{2}} \\log \\sin x d x\\)
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 19.
\nFind the following: \\(\\begin{array}{l}
\n\\text { (i) } \\int \\cot x \\log (\\sin x) d x \\\\
\n\\text { (ii) } \\int \\frac{1}{x^{2}+2 x+2} d x \\\\
\n\\text { (iii) } \\int x e^{9 x} d x
\n\\end{array}\\) (May – 2017)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

We hope the Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals help you. If you have any query regarding Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 7 Integrals. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 7 Integrals Plus Two Maths Application of Derivatives 3 Marks Important Questions Question […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\nPlus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals - A Plus Topper<\/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:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-7\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals\" \/>\n<meta property=\"og:description\" content=\"Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 7 Integrals. 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Here we have given Plus Two Maths Chapter Wise Previous Chapter 7 Integrals. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 7 Integrals Plus Two Maths Application of Derivatives 3 Marks Important Questions Question […]","og_url":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-7\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2019-04-24T05:21:27+00:00","article_modified_time":"2020-12-08T06:52:28+00:00","og_image":[{"url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-7-Integrals-1.png"}],"twitter_card":"summary","twitter_misc":{"Written by":"Kalyan","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-7\/#primaryimage","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-7-Integrals-1.png","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2020\/12\/Plus-Two-Maths-Chapter-Wise-Previous-Questions-Chapter-7-Integrals-1.png","width":365,"height":442,"caption":"Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals 1"},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-7\/#webpage","url":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-7\/","name":"Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals - 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