(March – 2015)<\/span>
\nAnswer:
\n<\/p>\nQuestion 4.
\nEvaluate \\(\\int_{0}^{x} \\log (1+\\cos x) d x\\)
\nAnswer:
\n<\/p>\n
Question 5.
\nFind \\(\\int_{0}^{5}(x+1) d x \\text { as limit of a sum. }\\)
\nAnswer:
\n<\/p>\n
Question 6.
\nEvaluate \\(\\int_{0}^{4} x^{2} d x\\) as the limit of a sum. (March – 2017)<\/span>
\nAnswer:
\n<\/p>\nPlus 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
\n<\/p>\nQuestion 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<\/p>\nQuestion 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
\n<\/p>\nQuestion 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<\/p>\nQuestion 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<\/p>\nQuestion 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
\n<\/p>\nQuestion 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
\n<\/p>\nQuestion 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<\/p>\nQuestion 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<\/p>\nQuestion 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
\n
\n<\/p>\nQuestion 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
\n
\n<\/p>\nQuestion 12.
\nEvaluate \\(\\int_{0}^{\\pi \/ 4} \\log (1+\\tan x) d x\\) (March – 2013)<\/span>
\nAnswer:
\n<\/p>\nQuestion 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
\n<\/p>\nQuestion 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
\n<\/p>\nQuestion 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<\/p>\nQuestion 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<\/p>\nQuestion 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
\n<\/p>\n
Question 18.
\nFind \\(\\int_{0}^{\\frac{\\pi}{2}} \\log \\sin x d x\\)
\nAnswer:
\n
\n<\/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<\/p>\nWe 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":"\n
Plus Two Maths Chapter Wise Previous Questions Chapter 7 Integrals - A Plus Topper<\/title>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\t\n\t\n\t\n