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Author: Tinku Tara

4-1-2-x-

Question Number 535 by kth last updated on 25/Jan/15 $$\int_{\mathrm{4}} ^{\mathrm{1}} \frac{\mathrm{2}}{\:\sqrt{{x}}} \\ $$ Answered by 13/NaSaNa(N)056565 last updated on 25/Jan/15 $$=\mathrm{2}\int_{\mathrm{4}} ^{\mathrm{1}} {x}^{\frac{−\mathrm{1}}{\mathrm{2}}} {dx}…

if-f-is-continuos-and-diferentiable-everywhere-on-R-if-f-0-0-and-f-x-f-x-then-proof-that-f-x-0-

Question Number 532 by 123456 last updated on 25/Jan/15 $${if}\:{f}\:{is}\:{continuos}\:{and}\:{diferentiable} \\ $$$${everywhere}\:{on}\:\mathbb{R},\:{if}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{and} \\ $$$$\mid{f}'\left({x}\right)\mid\leqslant\mid{f}\left({x}\right)\mid\:{then}\:{proof}\:{that} \\ $$$${f}\left({x}\right)=\mathrm{0} \\ $$ Answered by prakash jain last updated on…

Integrate-dx-ax-2-bx-c-y-ax-2-bx-c-y-dy-dx-2ax-b-d-b-2-4ac-d-d-Case-1-d-2-lt-0-I-2-d-tan-1-y-d-C-tan-1-arctan-Case-2-d-2-0-I-2-y-C-Case

Question Number 66066 by Kunal12588 last updated on 08/Aug/19 $${Integrate}\:\int\frac{{dx}}{{ax}^{\mathrm{2}} +{bx}+{c}} \\ $$$${y}\:=\:{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${y}'=\frac{{dy}}{{dx}}=\mathrm{2}{ax}+{b} \\ $$$${d}\:=\:\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}} \\ $$$${d}'\:=\:\sqrt{−{d}} \\ $$$${Case}\:\mathrm{1}.\:{d}^{\mathrm{2}} \:<\:\mathrm{0} \\…

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Question Number 66062 by mathmax by abdo last updated on 08/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{ch}\left({t}\right)+{xsh}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left({ch}\left({t}\right)+{xsh}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{ch}\left({t}\right)+\mathrm{3}{sh}\left({t}\right)}\:{and}\:\int_{\mathrm{0}}…