Question Number 208052 by necx122 last updated on 03/Jun/24 $${Sketch}\:{the}\:{curve}\:{y}\:=\:{x}^{\mathrm{3}} . \\ $$$$\left({a}\right)\:{Find}\:{the}\:{equation}\:{of}\:{the}\:{tangent} \\ $$$${to}\:{the}\:{curve}\:{at}\:{A}\left(\mathrm{1},\mathrm{1}\right). \\ $$$$\left({b}\right)\:{Find}\:{the}\:{coordinates}\:{of}\:{point}\:{B}, \\ $$$${where}\:{the}\:{tangent}\:{meets}\:{the}\:{curve}\:{again}. \\ $$$$\left({c}\right)\:{Calculate}\:{the}\:{area}\:{between}\:{the} \\ $$$${tangent}\:{B}\:{and}\:{the}\:{arc}\:{AB}\:{of}\:{the}\:{curve}. \\ $$…
Question Number 207949 by mnjuly1970 last updated on 31/May/24 $$ \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\:\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{6}} \boldsymbol{{x}}\:+\:\boldsymbol{{cos}}^{\mathrm{6}} \boldsymbol{{x}}}\:=\:?\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−− \\…
Question Number 207938 by necx122 last updated on 31/May/24 $${what}\:{is}\:{the}\:{area}\:{bounded}\:{by}\:{the}\:{curve} \\ $$$${y}={x}\left({x}−\mathrm{2}\right)\left({x}−\mathrm{5}\right)\:{and}\:{the}\:{x}\:{axis}? \\ $$$$ \\ $$ Answered by mr W last updated on 31/May/24 $${A}=\int_{\mathrm{0}}…
Question Number 207924 by AliJumaa last updated on 31/May/24 $$\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}\: \\ $$$${prove}\:{that}\:{right} \\ $$$${its}\:{a}\:{relation}\:{that}\:{i}\:{have}\:{derrived}…
Question Number 207906 by nachosam last updated on 30/May/24 $${help} \\ $$$$\int_{\mathrm{1}} ^{\:\infty} {x}^{−{ln}\left({x}\right)} {dx} \\ $$$$ \\ $$ Answered by Berbere last updated on…
Question Number 207878 by luciferit last updated on 29/May/24 Answered by Berbere last updated on 30/May/24 $${not}\:{well}\:{defind} \\ $$$$\left.{g}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {f}\left({t}^{\mathrm{4}} \right)+\mathrm{4}{t}^{\mathrm{4}} {f}'\left({t}\right)\right){dt}? \\ $$$$…
Question Number 207857 by necx122 last updated on 28/May/24 $$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$ Answered by Ghisom last updated on 28/May/24 $$\mathrm{by}\:\mathrm{parts} \\ $$$$\int{x}\mathrm{arctan}\:{x}\:{dx}= \\ $$$$=\frac{{x}^{\mathrm{2}}…
Question Number 207789 by Ghisom last updated on 26/May/24 $$\forall{r}\in\mathbb{R}:\:{H}_{{r}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{r}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$$${H}_{{r}+\mathrm{2}} −{H}_{{r}} =\mathrm{1} \\ $$$${r}=? \\ $$ Answered by MM42…
Question Number 207753 by efronzo1 last updated on 25/May/24 Answered by Berbere last updated on 25/May/24 $${A}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\frac{{k}+\mathrm{1}−{k}}{{k}\left({k}+\mathrm{1}\right)}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\frac{\mathrm{1}}{{k}}−\frac{\mathrm{1}}{{k}+\mathrm{1}} \\ $$$$=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2024}}=\frac{\mathrm{2023}}{\mathrm{2024}}…
Question Number 207707 by justenspi last updated on 23/May/24 $$\underset{\mathrm{0}} {\overset{+\infty} {\int}}\frac{\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)}{\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)+\left({x}\mathrm{cos}\:\left({x}\right)+\mathrm{sin}\:\left({x}\right)\right)^{\mathrm{2}} }{d}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com