Question Number 28756 by abdo imad last updated on 29/Jan/18 $${find}\:{in}\:{terms}\:{of}\:\lambda\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\lambda{t}} \:\frac{{sint}}{\:\sqrt{{t}}}\:{dt}\:\:{with}\:\:\lambda>\mathrm{0} \\ $$ Commented by abdo imad last updated on 30/Jan/18 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}}…
Question Number 94285 by mathmax by abdo last updated on 17/May/20 $${approximate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{{sinx}}{dx}\:{by}\:{simpsom}\:{method} \\ $$ Commented by PRITHWISH SEN 2 last updated on 18/May/20…
Question Number 159823 by tounghoungko last updated on 21/Nov/21 Answered by Ar Brandon last updated on 21/Nov/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}+{x}}}\mathrm{sin}^{−\mathrm{1}} {xdx}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\mathrm{sin}^{−\mathrm{1}} {xdx}…
Question Number 94286 by mhmd last updated on 17/May/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94278 by M±th+et+s last updated on 17/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{e}^{\sqrt{{x}}} }{\:\sqrt{{x}}}{dx} \\ $$ Commented by PRITHWISH SEN 2 last updated on 17/May/20 $$\mathrm{e}^{\sqrt{\mathrm{x}}}…
Question Number 94269 by LPM last updated on 17/May/20 Commented by prakash jain last updated on 17/May/20 $$\mathrm{ln}\:\left(\mathrm{1}+{x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{{n}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \\ $$$$\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}\right)}{{x}}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}}…
Question Number 94243 by mhmd last updated on 17/May/20 $${By}\:{using}\:{the}\:{double}\:{integral}\:{find}\:{the}\:{area}\:{of}\:{the}\:{regiin}\: \\ $$$${bounded}\:{by}\:{the}\:{curve}\:{y}={x}^{\mathrm{2}} +\mathrm{2}{x}\:,\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x}\:{and}\:{x}−{axis}\: \\ $$$$\left({sketch}\:{the}\:{region}\:{of}\:{integration}\right) \\ $$$${pleas}\:{sir}\:{help}\:{me}\: \\ $$ Commented by Ar Brandon last…
Question Number 28705 by students last updated on 29/Jan/18 $${solve}\:{the}\:{integrayion}\:\frac{{sin}\mathrm{2}{x}}{{sin}\mathrm{5}{xsin}\mathrm{3}{x}} \\ $$ Answered by mrW2 last updated on 30/Jan/18 $$\mathrm{sin}\:\mathrm{2}{x}=\mathrm{sin}\:\left(\mathrm{5}{x}−\mathrm{3}{x}\right)=\mathrm{sin}\:\mathrm{5}{x}\:\mathrm{cos}\:\mathrm{3}{x}−\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{sin}\:\mathrm{3}{x} \\ $$$$\int\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{sin}\:\mathrm{5}{x}\:\mathrm{sin}\:\mathrm{3}{x}}{dx}=\int\mathrm{cot}\:\mathrm{3}{x}\:{dx}−\int\mathrm{cot}\:\mathrm{5}{x}\:{dx} \\ $$$$=\frac{\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{3}{x}\right)}{\mathrm{3}}−\frac{\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{5}{x}\right)}{\mathrm{5}}+{C} \\…
Question Number 28706 by students last updated on 29/Jan/18 $${most}\:{important}\:{question}\:{gor}\:{boar}\:{or}\:{iit}\: \\ $$$${solve}\:{the}\:{integration}\:\:\frac{\mathrm{1}}{\mathrm{3}{sinx}+\mathrm{4}{cosx}} \\ $$ Commented by abdo imad last updated on 29/Jan/18 $${let}\:{put}\:{I}=\:\int\:\:\frac{{dx}}{\mathrm{3}{sinx}+\mathrm{4}{cosx}}\:{and}\:{use}\:{the}\:{ch}.\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t} \\ $$$${I}=\:\int\:\:\:\:\frac{\mathrm{1}}{\frac{\mathrm{6}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 28703 by students last updated on 29/Jan/18 $$\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\:\:{solve}\:{the}\:{integration} \\ $$ Commented by abdo imad last updated on 29/Jan/18 $${let}\:{put}\:{I}=\:\int\:\:\frac{{dx}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}}…