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Category: Integration

Question-54616

Question Number 54616 by cesar.marval.larez@gmail.com last updated on 07/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 08/Feb/19 $${a}={tanx}\:\:{da}={sec}^{\mathrm{2}} {xdx} \\ $$$$\int\frac{{a}^{\mathrm{2}} {da}}{\:\sqrt{\mathrm{2}+\mathrm{1}+{a}^{\mathrm{2}} }} \\ $$$$\int\frac{{a}^{\mathrm{2}} +\mathrm{3}−\mathrm{3}}{\:\sqrt{{a}^{\mathrm{2}}…

Question-185677

Question Number 185677 by Mingma last updated on 25/Jan/23 Answered by Frix last updated on 25/Jan/23 $$\frac{{df}}{{dx}}=\mathrm{e}^{\mid{x}\mid} −\mathrm{e}^{\mid{x}−\mathrm{2}\mid} =\mathrm{0}\:\Rightarrow\:{x}=\mathrm{1} \\ $$$${f}\left(\mathrm{1}\right)=\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\mathrm{e}^{\mid\mathrm{1}−{t}\mid} {dt}=\mathrm{2}\underset{\mathrm{0}} {\overset{\mathrm{1}}…

I-0-pi-2-1-ln-tan-r-1-1-tan-r-dr-

Question Number 120064 by bemath last updated on 29/Oct/20 $${I}\:=\:\int\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\:}}\left(\frac{\mathrm{1}}{\mathrm{ln}\:\left(\mathrm{tan}\:{r}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{tan}\:{r}}\:\right)\:{dr} \\ $$ Answered by mnjuly1970 last updated on 29/Oct/20 $$\mathrm{I}\overset{\int_{{a}} ^{\:{b}} {f}\left({x}\right){dx}=\int_{{a}} ^{\:{b}}…