Question Number 66150 by mathmax by abdo last updated on 09/Aug/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {sin}\left({x}^{\mathrm{3}} \right){dx}\: \\ $$ Commented by mathmax by abdo last…
Question Number 613 by 123456 last updated on 11/Feb/15 $$\Xi\left({a},{b},{c},{d}\right)=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}^{{a}} \left(\pi{x}\right)\mathrm{cos}^{{b}} \left(\pi{x}\right)}{{x}^{{c}} \left(\mathrm{1}−{x}\right)^{{d}} }{dx} \\ $$$$\Xi\left(\mathrm{1},\mathrm{1},\mathrm{1},\mathrm{1}\right)=? \\ $$ Commented by prakash jain last…
Question Number 131678 by liberty last updated on 07/Feb/21 $$\:\mathrm{Nice}\:\mathrm{calculus}\: \\ $$$$\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{n}−\mathrm{2}} \:−\mathrm{1}}{\mathrm{x}^{\mathrm{n}} \:+\mathrm{1}}\:\mathrm{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 131673 by liberty last updated on 07/Feb/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\mathrm{x}\right)}{\mathrm{ln}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by mindispower last updated on 07/Feb/21 $${ln}\left({x}\right)=−{t} \\…
Question Number 604 by 123456 last updated on 09/Feb/15 $$\underset{\mathrm{0}} {\overset{+\mathrm{1}} {\int}}\left(\underset{−\mathrm{1}} {\overset{+\mathrm{1}} {\int}}\frac{\mathrm{1}−{x}^{\mathrm{4}} {y}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{2}} {y}}{dx}\right){dy} \\ $$ Answered by prakash jain last updated…
Question Number 601 by 123456 last updated on 08/Feb/15 $$\underset{\mathrm{0}} {\overset{+\mathrm{1}} {\int}}\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{1}}{dx} \\ $$ Answered by prakash jain last updated on 08/Feb/15 $$\int_{\mathrm{0}}…
Question Number 597 by 112358 last updated on 08/Feb/15 $${Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}+{u}^{\mathrm{4}} }{du}\:{exactly}\:{if}\: \\ $$$${u}={coshx}.\: \\ $$ Commented by prakash jain last updated on 08/Feb/15…
Question Number 131674 by liberty last updated on 07/Feb/21 $$\mathrm{Given}\:\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{satisfies}\: \\ $$$$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\sqrt{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{y}^{\mathrm{2}} −\mathrm{1}\right)}}{\mathrm{xy}}\:=\:\mathrm{1}\: \\ $$$$\mathrm{lies}\:\mathrm{at}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{1}\right)\:\mathrm{and}\:\left(\sqrt{\mathrm{2}}\:,\mathrm{k}\right). \\ $$$$\mathrm{find}\:\mathrm{k}\:. \\ $$ Terms of Service Privacy Policy…
Question Number 571 by 123456 last updated on 30/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$$\:{if}\:{f},{g}\:{are}\:{continuos}\:{into}\:\left[{a},{b}\right]\:{and} \\ $$$${g}\:{never}\:{change}\:{sign}\:{into}\:\left[{a},{b}\right]\:{then} \\ $$$$\exists{c}\in\left[{a},{b}\right]\:{such}\:{that} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}{f}\left({x}\right){g}\left({x}\right){dx}={f}\left({c}\right)\underset{{a}} {\overset{{b}} {\int}}{g}\left({x}\right){dx} \\ $$ Answered…
Question Number 570 by defgd last updated on 28/Jan/15 $$\int\:\frac{\mathrm{1}+{x}}{\left(\mathrm{2}+{x}\right)^{\mathrm{2}} }\:{e}^{{x}} \:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com