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Category: Integration

x-3-5-2x-2-2-dx-

Question Number 208205 by efronzo1 last updated on 07/Jun/24 $$\:\:\:\int\:\left({x}^{\mathrm{3}} .\:\mathrm{5}^{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}} \:\right)\:{dx}\:=? \\ $$ Answered by Frix last updated on 07/Jun/24 $$\int{x}^{\mathrm{3}} \mathrm{5}^{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}}…

find-4-dx-x-1-3-x-3-5-

Question Number 208062 by mathzup last updated on 03/Jun/24 $${find}\:\:\int_{\mathrm{4}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$ Answered by Frix last updated on 03/Jun/24 $$\mathrm{Use}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\left(\mathrm{search}\:\mathrm{it}\:\mathrm{on}\right. \\…

Sketch-the-curve-y-x-3-a-Find-the-equation-of-the-tangent-to-the-curve-at-A-1-1-b-Find-the-coordinates-of-point-B-where-the-tangent-meets-the-curve-again-c-Calculate-the-area-between-the

Question Number 208052 by necx122 last updated on 03/Jun/24 $${Sketch}\:{the}\:{curve}\:{y}\:=\:{x}^{\mathrm{3}} . \\ $$$$\left({a}\right)\:{Find}\:{the}\:{equation}\:{of}\:{the}\:{tangent} \\ $$$${to}\:{the}\:{curve}\:{at}\:{A}\left(\mathrm{1},\mathrm{1}\right). \\ $$$$\left({b}\right)\:{Find}\:{the}\:{coordinates}\:{of}\:{point}\:{B}, \\ $$$${where}\:{the}\:{tangent}\:{meets}\:{the}\:{curve}\:{again}. \\ $$$$\left({c}\right)\:{Calculate}\:{the}\:{area}\:{between}\:{the} \\ $$$${tangent}\:{B}\:{and}\:{the}\:{arc}\:{AB}\:{of}\:{the}\:{curve}. \\ $$…

Find-the-value-of-0-2-dx-sin-6-x-cos-6-x-

Question Number 207949 by mnjuly1970 last updated on 31/May/24 $$ \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\:\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{6}} \boldsymbol{{x}}\:+\:\boldsymbol{{cos}}^{\mathrm{6}} \boldsymbol{{x}}}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−− \\…

f-x-g-x-dx-n-0-1-n-lim-h-0-1-h-n-i-o-n-1-i-n-i-n-i-f-x-n-i-h-1-n-a-x-x-t-n-g-t-dt-prove-that-right-its-a-relation-that-i-have-derrived-

Question Number 207924 by AliJumaa last updated on 31/May/24 $$\int{f}\left({x}\right){g}\left({x}\right){dx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{{n}} \:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{h}^{{n}} }\:\underset{{i}={o}} {\overset{{n}} {\sum}}\left[\:\left(−\mathrm{1}\right)^{{i}} \left(\frac{{n}!}{{i}!\left({n}−{i}\right)!}\right){f}\left({x}+\left({n}−{i}\right){h}\right)\right]\:\frac{\mathrm{1}}{{n}!}\underset{{a}} {\overset{{x}} {\int}}\left({x}−{t}\right)^{{n}} {g}\left({t}\right){dt}\: \\ $$$${prove}\:{that}\:{right} \\ $$$${its}\:{a}\:{relation}\:{that}\:{i}\:{have}\:{derrived}…