Question Number 133719 by leena12345 last updated on 23/Feb/21 Commented by leena12345 last updated on 23/Feb/21 $${help} \\ $$ Answered by bramlexs22 last updated on…
Question Number 2629 by Filup last updated on 24/Nov/15 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{evalate}: \\ $$$${A}=\int_{{a}} ^{\:{b}} \lfloor{f}\left({x}\right)\rfloor{dx} \\ $$$$ \\ $$$${for}\:{example}: \\ $$$$\int_{\mathrm{0}.\mathrm{5}} ^{\:\mathrm{2}.\mathrm{5}} \lfloor{x}^{\mathrm{2}} \rfloor{dx} \\ $$…
Question Number 68149 by ~ À ® @ 237 ~ last updated on 06/Sep/19 $$\:{Explicit}\:\:\:{f}\left({a}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left({an}+\mathrm{1}\right)}\:\:\:\: \\ $$ Commented by turbo msup by…
Question Number 68145 by Joel122 last updated on 06/Sep/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{length},\:\mathrm{given}\:\mathrm{the}\:\mathrm{curve} \\ $$$${x}\left({t}\right)\:=\:\mathrm{sin}\:\left(\pi{t}\right),\:\:{y}\left({t}\right)\:=\:{t}\:,\:\:\mathrm{0}\:\leqslant\:{t}\:\leqslant\:\mathrm{1} \\ $$ Commented by Joel122 last updated on 06/Sep/19 $${x}'\left({t}\right)\:=\:\pi\:\mathrm{cos}\:\left(\pi{t}\right),\:{y}'\left({t}\right)\:=\:\mathrm{1} \\ $$$$ \\…
Question Number 68141 by MJS last updated on 06/Sep/19 $$\mathrm{the}\:\mathrm{2}\:\mathrm{formulas}\:\mathrm{for}\:\mathrm{solving}\:\int\frac{{dx}}{{x}^{\mathrm{3}} +{px}+{q}}\:\mathrm{with} \\ $$$$“\mathrm{nasty}''\:\mathrm{solutions}\:\mathrm{of}\:{x}^{\mathrm{3}} +{px}+{q}=\mathrm{0}\:\mathrm{with}\:{p},\:{q}\:\in\mathbb{R} \\ $$$$ \\ $$$$\mathrm{case}\:\mathrm{1} \\ $$$${D}=\frac{{p}^{\mathrm{3}} }{\mathrm{27}}+\frac{{q}^{\mathrm{2}} }{\mathrm{4}}>\mathrm{0}\:\Rightarrow\:{x}^{\mathrm{3}} +{px}+{q}=\mathrm{0}\:\mathrm{has}\:\mathrm{got}\:\mathrm{1}\:\mathrm{real} \\ $$$$\mathrm{and}\:\mathrm{2}\:\mathrm{conjugated}\:\mathrm{complex}\:\mathrm{solutions}…
Question Number 133674 by liberty last updated on 23/Feb/21 $$\int\:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{x}}}}\:\mathrm{dx}\:=?\: \\ $$ Answered by EDWIN88 last updated on 23/Feb/21 $$\:\mathrm{let}\:\mathrm{y}\:=\:\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{x}}}}\:\Rightarrow\sqrt{\mathrm{1}+\sqrt{\mathrm{x}}}\:=\:\mathrm{y}^{\mathrm{2}} −\mathrm{1} \\ $$$$\Rightarrow\mathrm{1}+\sqrt{\mathrm{x}}\:=\:\mathrm{y}^{\mathrm{4}} −\mathrm{2y}^{\mathrm{2}} +\mathrm{1}\:,\:\mathrm{x}\:=\:\left(\mathrm{y}^{\mathrm{4}}…
Question Number 68116 by aliesam last updated on 05/Sep/19 $$\int\frac{{dx}}{{sin}\mathrm{2}{x}−{sec}\left({x}\right)} \\ $$ Commented by MJS last updated on 06/Sep/19 $$\mathrm{look}\:\mathrm{at}\:\mathrm{question}\:\mathrm{68141} \\ $$ Answered by MJS…
Question Number 68100 by ~ À ® @ 237 ~ last updated on 04/Sep/19 $${Find}\:\:{K}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}−{t}+{t}^{\mathrm{2}} \right)}{{t}}\:{dt}\:\:\:\:\: \\ $$ Commented by mind is power…
Question Number 68094 by mhmd last updated on 04/Sep/19 $$\int{dx}/\sqrt[{{x}}]{\left(\pi+{e}\right)^{{x}^{\mathrm{2}} } }\: \\ $$ Answered by MJS last updated on 05/Sep/19 $$\int\frac{{dx}}{\:\sqrt[{{x}}]{\left(\pi+\mathrm{e}\right)^{{x}^{\mathrm{2}} } }}=\int\frac{{dx}}{\left(\pi+\mathrm{e}\right)^{{x}} }=−\frac{\mathrm{1}}{\left(\pi+\mathrm{e}\right)^{{x}}…
Question Number 68095 by mhmd last updated on 04/Sep/19 $$\int\sqrt{{x}}/\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}\:}\:{dx} \\ $$ Answered by MJS last updated on 05/Sep/19 $$\int\frac{{x}^{\mathrm{1}/\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{1}/\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}={x}^{\mathrm{1}/\mathrm{6}} \:\rightarrow\:{dx}=\mathrm{6}{x}^{\mathrm{5}/\mathrm{6}}…