{"id":19338,"date":"2020-01-10T16:00:39","date_gmt":"2020-01-10T10:30:39","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=19338"},"modified":"2021-07-02T15:29:44","modified_gmt":"2021-07-02T09:59:44","slug":"2nd-puc-basic-maths-question-bank-chapter-20-ex-20-1","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-question-bank-chapter-20-ex-20-1\/","title":{"rendered":"2nd PUC Basic Maths Question Bank Chapter 20 Indefinite Integrals Ex 20.1"},"content":{"rendered":"

Students can Download Basic Maths Exercise 20.1 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Basic Maths Question Bank Chapter 20 Indefinite Integrals Ex 20.1<\/h2>\n

Part-A<\/span><\/p>\n

2nd PUC Basic Maths Indefinite Integrals Ex 20.1 One Mark Questions and Answers<\/strong><\/p>\n

Question 1.
\n\\(x^{2}-\\frac{6}{x}+5 e^{x}\\)
\nAnswer:
\n\\(\\int x^{2}-\\frac{6}{x}+5 e^{x} d x=\\frac{x^{3}}{3}-6 \\log x+5 e^{x}+C\\)<\/p>\n

Question 2.
\n7x<\/sup> – 10.9x<\/sup>
\nAnswer:
\n\\(\\int 7^{x}-10 \\cdot 9^{x} d x=\\frac{7^{x}}{\\log 7}-10 \\frac{9^{x}}{\\log 9}+C\\) [\u2235 aloge<\/sub>x<\/sup> = xa<\/sup>]<\/p>\n

Question 3.
\nxe<\/sup> + ex<\/sup> – log a
\nAnswer:
\n\\(\\int\\left(x^{e}+e^{x}-\\log a\\right) d x=\\frac{x^{e+1}}{e+1}+e^{x}-\\log a \\cdot x+c\\)<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\n76log7<\/sub>x<\/sup>.
\nAnswer:
\n\\(\\int 7^{6 \\log _{e} x} d x=\\int 7^{\\log _{7} x^{6}} d x=\\int x^{6} d x=\\frac{x^{7}}{7}+c\\)<\/p>\n

Question 5.
\ncot2<\/sup>x.
\nAnswer:
\n\u222bcot2<\/sup>x dx = \u222b(cosec2<\/sup>x – 1)dx = cot x – x + c<\/p>\n

Question 6.
\n\\(\\frac{9 \\cos x}{5 \\sin ^{2} x}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 7.
\n7x2<\/sup> – 4 sec2<\/sup>x
\nAnswer:
\n\u222b7x2<\/sup> – 4 sec2<\/sup>x dx = 7.\\(\\frac{x^{3}}{3}\\) – 4.tan x + c<\/p>\n

Part-B<\/span><\/p>\n

2nd PUC Basic Maths Indefinite Integrals Ex 20.1 Two marks Questions and Answers<\/strong><\/p>\n

Question 1.
\n\\(\\int \\frac{x^{5}+5 x^{2}-7 x}{\\sqrt{x}}\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 2.
\n\\(\\left(x-\\frac{1}{x}\\right)^{2}\\)
\nAnswer:
\n\\(\\int\\left(x-\\frac{1}{x}\\right)^{2} d x=\\int\\left(x^{2}+\\frac{1}{x^{2}}-2\\right) d x=\\frac{x^{3}}{3}-\\frac{1}{x}-2 x+c\\)<\/p>\n

Question 3.
\n\\(\\int \\sqrt{x}\\left(1-\\frac{1}{\\sqrt{x}}\\right)\\)
\nAnswer:
\n\\(\\int \\sqrt{x}\\left(1-\\frac{1}{\\sqrt{x}}\\right) d x=\\int(\\sqrt{x}-1) d x=\\frac{2}{3} x^{\\frac{3}{2}}-x+c\\)<\/p>\n

Question 4.
\n\\(\\int x^{\\frac{3}{2}}\\left(x^{1}-\\frac{1}{x^{2}}\\right)\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 5.
\n\\(\\int \\frac{6^{x}-3^{x}}{5^{x}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 6.
\n\u222b(33log3<\/sub>x<\/sup> – 77log7<\/sub>x<\/sup>)
\nAnswer:
\n\u222b(33log3<\/sub>x<\/sup> – 77log7<\/sub>x<\/sup>)dx = \u222b(x3<\/sup> – x7<\/sup>)dx = \\(\\frac{x^{4}}{4}-\\frac{x^{8}}{8}\\) + C [\u2235 aaloga<\/sub>x<\/sup> = xa<\/sup>]<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\n\\(\\sqrt{1-\\cos 2 x}\\)
\nAnswer:
\n\\(\\int \\sqrt{1-\\cos 2 x \\cdot d x}=\\int \\sqrt{2 \\sin ^{2} x} d x=\\int \\sqrt{2} \\cdot \\sin x \\cdot d x=\\sqrt{2} \\cos x+c\\)<\/p>\n

Question 8.
\n\\(\\frac{1+\\sin x}{\\cos ^{2} x}\\)
\nAnswer:
\n\\(\\int \\frac{1+\\sin x}{\\cos ^{2} x} d x=\\int \\frac{1}{\\cos ^{2} x} d x+\\frac{\\sin x}{\\cos ^{2} x} d x=\\int \\sec ^{2} x+\\tan x \\cdot \\sec x d x=\\tan x+\\sec x+c\\)<\/p>\n

Question 9.
\nsec x(sec x – tan x)
\nAnswer:
\n\u222bsec x (sec x – tan x)dx = \u222bsec2<\/sup>x – sec x .tan x. dx
\n= tan x – sec x + c<\/p>\n

Part-c<\/span><\/p>\n

Integrate the following<\/span><\/p>\n

2nd PUC Basic Maths Indefinite Integrals Ex 20.1 Three marks Questions and Answers<\/strong><\/p>\n

Question 1.
\n\\(\\frac{\\left(a^{x}+b^{x}\\right)^{2}}{a^{x} b^{x}}\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 2.
\n\\(\\csc x \\cdot \\sqrt{\\csc ^{2} x-1}\\)
\nAnswer:
\n\\(\\int \\csc x \\cdot \\sqrt{\\csc ^{2} x-1} \\cdot d x\\)
\n= \u222bcos ex. \\(\\sqrt{\\cot ^{2} x} d x\\) = \u222bcosecx. cot x .dx = cosec x + c<\/p>\n

Question 3.
\n\\(\\sqrt{1+\\sin 2 x}\\)
\nAnswer:
\n\\(\\int \\sqrt{1+\\sin 2 x} d x=\\int \\sqrt{(\\cos x+\\sin x)^{2}}=\\int(\\cos x+\\sin x) d x\\)
\n= sinx – cosx + c<\/p>\n

Question 4.
\n\\(\\frac{1-\\cos 2 x}{1+\\cos 2 x}\\)
\nAnswer:
\n\"2nd<\/p>\n

Part-D<\/span><\/p>\n

Integrate the following<\/span><\/p>\n

2nd PUC Basic Maths Indefinite Integrals Ex 20.1<\/strong> Five Marks Questions and Answers<\/strong><\/p>\n

Question 1.
\n\\(\\frac{1}{1+\\sin x}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 2.
\n\\(\\frac{\\sec x}{1+\\sec x}\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\n\\(\\frac{\\cos x}{1+\\cos x}\\)
\nAnswer:
\n\\(\\int \\frac{\\cos x}{1+\\cos x} d x=\\int \\frac{\\cos x(1-\\cos x)}{1-\\cos ^{2} x} d x=\\int \\frac{\\cos x}{\\sin ^{2} x}-\\frac{\\cos ^{2} x}{\\sin ^{2} x} d x\\)
\n= \u222b(cot x . cosecx – cot 2<\/sup>)dx
\n= -cosec x – \u222b(cosec2<\/sup>x – 1)dx
\n= -cosecx -(- cotx) + x + c
\n= -cosecx + cot x + x + c<\/p>\n

Question 4.
\n\\(\\frac{\\sin ^{2} x}{1+\\cos x}\\)
\nAnswer:
\n\"2nd
\n= \u222b(1 – cos x)dx
\n= x – sinx + c<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Basic Maths Exercise 20.1 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Basic Maths Question Bank Chapter 20 Indefinite Integrals Ex 20.1 Part-A 2nd PUC Basic Maths …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/19338"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=19338"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/19338\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=19338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=19338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=19338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}