Question Number 124135 by bramlexs22 last updated on 01/Dec/20 $$\:{B}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:\left[\sqrt{\frac{\mathrm{4}−{x}}{{x}}}\:−\:\sqrt{\frac{{x}}{\mathrm{4}−{x}}}\:\right]\:{dx} \\ $$ Answered by nico last updated on 01/Dec/20 $$=\int_{\mathrm{0}} ^{\mathrm{2}} \frac{\mathrm{4}−{x}−{x}}{\:\sqrt{\mathrm{4}{x}−{x}^{\mathrm{2}} }}{dx}=\int_{\mathrm{0}}…
Question Number 58595 by rahul 19 last updated on 25/Apr/19 Answered by tanmay last updated on 26/Apr/19 $${a}={x}^{\mathrm{2}} \rightarrow{da}=\mathrm{2}{xdx} \\ $$$${xdx}=\frac{{da}}{\mathrm{2}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{100}} \left\{{a}\right\}×\frac{{da}}{\mathrm{2}}\rightarrow{I}_{\mathrm{2}}…
Question Number 189639 by mnjuly1970 last updated on 19/Mar/23 $$ \\ $$$$\:\:\begin{pmatrix}{\mathrm{20}}\\{\:\mathrm{0}}\end{pmatrix}\:\begin{pmatrix}{\mathrm{10}}\\{\:\mathrm{1}}\end{pmatrix}\:+\:\begin{pmatrix}{\mathrm{20}}\\{\:\mathrm{1}}\end{pmatrix}\:\begin{pmatrix}{\mathrm{10}}\\{\:\:\mathrm{2}}\end{pmatrix}\:+…+\:\begin{pmatrix}{\:\:\:\mathrm{20}}\\{\:\:\mathrm{9}}\end{pmatrix}\:\begin{pmatrix}{\:\:\mathrm{10}}\\{\:\mathrm{10}}\end{pmatrix}\:=? \\ $$$$ \\ $$ Commented by cortano12 last updated on 21/Mar/23 $$\:=\:\begin{pmatrix}{\mathrm{30}}\\{\:\:\mathrm{9}}\end{pmatrix}\:=\frac{\mathrm{30}.\mathrm{29}.\mathrm{28}.\mathrm{27}.\mathrm{26}.\mathrm{25}.\mathrm{24}.\mathrm{23}.\mathrm{22}}{\mathrm{9}.\mathrm{8}.\mathrm{7}.\mathrm{6}.\mathrm{5}.\mathrm{4}.\mathrm{3}.\mathrm{2}.\mathrm{1}} \\…
Question Number 124101 by Ar Brandon last updated on 30/Nov/20 $$\int\left(\frac{\mathrm{x}^{−\mathrm{6}} −\mathrm{64}}{\mathrm{4}+\mathrm{2x}^{−\mathrm{1}} +\mathrm{x}^{−\mathrm{2}} }\centerdot\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{4}−\mathrm{4x}^{−\mathrm{1}} +\mathrm{x}^{−\mathrm{2}} }−\frac{\mathrm{4x}^{\mathrm{2}} \left(\mathrm{2x}+\mathrm{1}\right)}{\mathrm{1}−\mathrm{2x}}\right)\mathrm{dx} \\ $$ Answered by MJS_new last updated…
Question Number 124062 by Bird last updated on 30/Nov/20 $${find}\:\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sin}\left({nx}\right)}{{sin}^{{n}} \left({x}\right)}{dx}\:\:\:\left({n}\:{natural}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124063 by Bird last updated on 30/Nov/20 $${find}\:\:\int\int_{{D}} \frac{{arctan}\left(\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)}{{x}+{y}}{dxdy} \\ $$$${D}=\left\{\left({x},{y}\right)\:/\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124061 by Bird last updated on 30/Nov/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{xarctanx}}{\left({x}^{\mathrm{2}\:} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by mnjuly1970 last updated on 30/Nov/20 $$\Omega=\left[\frac{−\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{tan}^{−\mathrm{1}}…
Question Number 124059 by Bird last updated on 30/Nov/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{3}} {sin}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124046 by john_santu last updated on 30/Nov/20 $$\:\:\phi\left(\alpha\right)\:=\:\int\:\frac{\mathrm{6}\alpha^{\mathrm{2}} +\mathrm{30}\alpha+\mathrm{2}}{\mathrm{4}\alpha^{\mathrm{2}} +\mathrm{20}\alpha+\mathrm{25}}\:{d}\alpha\: \\ $$ Answered by liberty last updated on 30/Nov/20 $$\:\phi\left(\alpha\right)\:=\:\int\:\frac{\mathrm{6}\alpha^{\mathrm{2}} +\mathrm{30}\alpha+\mathrm{2}}{\left(\mathrm{2}\alpha+\mathrm{5}\right)^{\mathrm{2}} }\:{d}\alpha \\…
Question Number 124043 by liberty last updated on 30/Nov/20 $$\:\int\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{2}{x}}\:{dx}\: \\ $$ Answered by john_santu last updated on 30/Nov/20 Answered by Dwaipayan Shikari last updated…