Integration – Page 870

Compute-0-1-x-1-logx-dx-

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Question Number 1613 by 112358 last updated on 26/Aug/15 $Compute$ $\int_{0}^{1} \frac{x - 1}{l o g x} d x .$ Commented by 123456 last updated on 27/Aug/15 $$\mathrm{I}=\mathrm{ln}\:\mathrm{10}\:\mathrm{ln}\:\mathrm{2} \…

find-the-area-abounded-y-x-and-y-x-2-

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Question Number 67138 by mhmd last updated on 23/Aug/19 $f i n d t h e a r e a a b o u n d e d y = \sqrt{x}$ $a n d y = x - 2 ?$ Commented by mr W last updated on 23/Aug/19 $s i r : y o u {d o n}^{'} t n e e d t o r e p e a t t h e$ $${same}\:{question}\:{so}\:{frequently}.…

Show-that-d-dy-g-1-y-g-2-y-f-x-y-dx-g-1-y-g-2-y-f-y-x-y-dx-g-2-y-f-g-2-y-y-g-1-y-f-g-1-y-y-using-Leibniz-s-rule-and-the-chain-rule-where-g-1-and-g-2-are-dif

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Question Number 1602 by 112358 last updated on 25/Aug/15 $S h o w t h a t$ $$\frac{{d}}{{dy}}\int_{{g}_{\mathrm{1}} \left({y}\right)} ^{{g}_{\mathrm{2}} \left({y}\right)} {f}\left({x},{y}\right){dx}=\int_{{g}_{\mathrm{1}} \left({y}\right)} ^{{g}_{\mathrm{2}} \left({y}\right)} \frac{\partial{f}}{\partial{y}}\left({x},{y}\right){dx}+{g}_{\mathrm{2}} ^{'} \left({y}\right){f}\left({g}_{\mathrm{2}} \left({y}\right),{y}\right)−{g}_{\mathrm{1}} ^{'} \left({y}\right){f}\left({g}_{\mathrm{1}}…

Let-and-denote-functions-of-x-where-is-odd-and-is-even-x-R-Is-it-generally-true-that-integrating-an-odd-function-gives-an-even-function-and-vice-versa-1-x-dx-1-x-C-and-2-x-d

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Question Number 1582 by 112358 last updated on 21/Aug/15 $L e t ϕ a n d ε d e n o t e f u n c t i o n s o f x$ $w h e r e ϕ i s o d d a n d ε i s e v e n \forall x \in R .$ $I s i t g e n e r a l l y t r u e t h a t i n t e g r a t i n g$ $a n o d d f u n c t i o n g i v e s a n e v e n$ $f u n c t i o n a n d v i c e v e r s a ?$ $\int ϕ_{1} (x) d x = ε_{1} (x) + C ?$ $${and}\:\int\phi_{\mathrm{2}} \left({x}\right){dx}=\varepsilon_{\mathrm{2}}…

find-the-area-abounded-y-x-afind-y-x-2-

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Question Number 67106 by mhmd last updated on 22/Aug/19 $f i n d t h e a r e a a b o u n d e d y = \sqrt{x}$ $a f i n d y = x - 2 ?$ Commented by kaivan.ahmadi last updated on 24/Aug/19 $x - 2 = \sqrt{x} \Rightarrow x^{2} - 5 x + 4 = 0 \Rightarrow (x - 1) (x - 4) = 0 \Rightarrow$ $$ ${\begin{cases} x = 1 \\ x = 2 \end{cases}$ …

find-the-area-abounded-y-x-afind-y-x-2-

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Question Number 67105 by mhmd last updated on 22/Aug/19 $f i n d t h e a r e a a b o u n d e d y = \sqrt{x}$ $a f i n d y = x - 2 ?$ Terms of Service Privacy Policy Contact: info@tinkutara.com

sin-2-x-1-sin-2-x-dx-

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Question Number 132610 by liberty last updated on 15/Feb/21 $Ω = \int \frac{\sin^{2} (x)}{1 + \sin^{2} (x)} dx$ Answered by Dwaipayan Shikari last updated on 15/Feb/21 $$\int\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}+{sin}^{\mathrm{2}} {x}}{dx}={x}−\int\frac{\mathrm{1}}{\mathrm{1}+{sin}^{\mathrm{2}}…

Question-67070

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Question Number 67070 by mRDv143 last updated on 22/Aug/19 Commented by Prithwish sen last updated on 23/Aug/19 $$\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \:\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}}}\:\mathrm{dx}=\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} .\mathrm{x}\:\sqrt{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{1}}}\:\mathrm{dx} \…

Question-132600

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Question Number 132600 by Ahmed1hamouda last updated on 15/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-67069

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Question Number 67069 by mRDv143 last updated on 22/Aug/19 Commented by Prithwish sen last updated on 22/Aug/19 $\int \frac{{(1 + logx)}^{2}}{1 + xlogx + logx + x {(logx)}^{2}} dx$ $= \int \frac{{(1 + logx)}^{2}}{(1 + logx) (1 + xlogx)} dx$ $$=\int\frac{\mathrm{1}+\mathrm{logx}}{\mathrm{1}+\mathrm{xlogx}}\:\mathrm{dx}\:\:\mathrm{put}\:\mathrm{1}+\mathrm{xlogx}\:=\:\mathrm{u}\Rightarrow\left(\mathrm{1}+\mathrm{logx}\right)\mathrm{dx}=\:\mathrm{du}…

Category: Integration