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Category: Integration

Question-44441

Question Number 44441 by Tawa1 last updated on 29/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18 $$\underset{{t}\rightarrow\mathrm{0}\:} {\mathrm{lim}}\:\frac{{e}^{−\mathrm{5}{t}} −\mathrm{1}}{−\mathrm{5}{t}}×−\mathrm{5} \\ $$$$=\mathrm{1}×−\mathrm{5}=−\mathrm{5} \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{t}^{\mathrm{11}} }{{t}^{\mathrm{11}}…

by-considering-a-sermicircle-from-r-to-r-prove-that-area-of-circle-is-pir-2-

Question Number 44424 by peter frank last updated on 28/Sep/18 $${by}\:{considering}\:\:{a}\:{sermicircle}\:{from}\:−{r}\:{to}\:\:{r}\:{prove}\:{that}\:{area}\:{of}\:{circle}\:{is}\:\pi{r}^{\mathrm{2}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18 $$\mathrm{2}\int_{−{r}} ^{{r}} \sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }\:\:{dx}…

Question-109949

Question Number 109949 by mnjuly1970 last updated on 26/Aug/20 Answered by mathdave last updated on 26/Aug/20 $${solution} \\ $$$${I}=\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\frac{\mathrm{sin}{x}}{\mathrm{cos}{x}}+\frac{\mathrm{cos}{x}}{\mathrm{sin}{x}}\right){dx}=\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\frac{\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{cos}{x}\mathrm{sin}{x}}\right){dx}…

Question-175471

Question Number 175471 by mnjuly1970 last updated on 31/Aug/22 Answered by Ar Brandon last updated on 31/Aug/22 $$\Omega=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sin2}{x}\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{cos}{x}\right){dx}=\mathrm{2}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sin}{x}\mathrm{cos}{x}\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{cos}{x}\right){dx} \\…

Question-175467

Question Number 175467 by manish54 last updated on 31/Aug/22 Commented by Frix last updated on 01/Sep/22 $$\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} }=\left[\mathrm{sinh}\:{x}\right]_{\mathrm{1}} ^{\infty} \:\mathrm{does}\:\mathrm{not}\:\mathrm{converge} \\ $$$$\underset{\mathrm{1}}…