Category: Integration

Question Number 65581 by aliesam last updated on 31/Jul/19 Commented by mathmax by abdo last updated on 31/Jul/19 $${let}\:{A}\:=\int\:{e}^{\left(\frac{\mathrm{1}}{{x}}−{x}\right)} \:{dx}\:\:\:{we}\:{have}\:{e}^{{u}} \:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{u}^{{n}} }{{n}!}\:\:{with}\:{radius}\:{infinite}\Rightarrow \…

Question Number 33 by user2 last updated on 25/Jan/15 $$\mathrm{Evaluate}\int \sin x\sqrt{1-\cos 2x}dx.$$ Answered by user2 last updated on 03/Nov/14 $$\int \sin x\sqrt{1-\cos 2x}dx$$$$=\int \sin x\cdot \sqrt{{2\sin }^{2}x}dx$$$$=\sqrt{\mathrm{2}}\int\mathrm{sin}^{\mathrm{2}}…

Question Number 131073 by Algoritm last updated on 01/Feb/21 Answered by mr W last updated on 01/Feb/21 $$F{}^{\prime }\left(x\right)=e^{{\left(\ln x\right)}^{100}}\frac{1}{x}$$$${F}\:'\left({e}\right)={e}^{\left(\mathrm{ln}\:{e}\right)^{\mathrm{100}} } \frac{\mathrm{1}}{{e}}={e}×\frac{\mathrm{1}}{{e}}=\mathrm{1} \…

Question Number 13004 by Nayon last updated on 10/May/17 $$If\int f\left(x\right)dx=g\left(x\right),thenwhy$$$${\int }_b^{a}f\left(x\right)dx=g\left(a\right)-g\left(b\right)???$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 144064 by 0731619 last updated on 21/Jun/21 Answered by MJS_new last updated on 21/Jun/21 $$\mathrm{simply}\mathrm{let}t=\tan x$$$$\Rightarrow \mathrm{answer}\mathrm{is}$$$$−\frac{{x}}{{b}^{\mathrm{2}} }+\frac{\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{{ab}^{\mathrm{2}} }\mathrm{arctan}\:\frac{{a}\mathrm{tan}\:{x}}{\:\sqrt{{a}^{\mathrm{2}}…