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Category: Integration

Question-202882

Question Number 202882 by dimentri last updated on 05/Jan/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by cortano12 last updated on 05/Jan/24 $$\:\:\begin{cases}{\mathrm{5}\underset{\mathrm{3}} {\overset{\mathrm{6}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{10}}\\{\mathrm{5}\underset{\mathrm{1}} {\overset{\mathrm{6}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{2}}\end{cases} \\…

3-4-5-x-4-6-x-1-dx-1-2-2x-1-find-the-value-of-x-Solution-4-5-x-3-4-6-x-2-2-x-k

Question Number 202636 by ibroclex_adex last updated on 30/Dec/23 $$\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\:^{\mathrm{3}} \sqrt{\mathrm{4}^{\mathrm{5}−\mathrm{x}} }}{\int_{\mathrm{4}} ^{\mathrm{6}} \left(\mathrm{x}−\mathrm{1}\right){dx}}\:=\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2x}−\mathrm{1}} }\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\mathrm{Solution}}…

If-I-n-denotes-z-n-e-1-z-dz-then-show-that-n-1-I-n-I-0-e-1-z-1-z-2-2-z-3-n-z-n-1-

Question Number 202592 by Calculusboy last updated on 30/Dec/23 $$\:\boldsymbol{{If}}\:\:\boldsymbol{{I}}_{\boldsymbol{{n}}} \:\boldsymbol{{denotes}}\:\int\boldsymbol{{z}}^{\boldsymbol{{n}}} \boldsymbol{{e}}^{\frac{\mathrm{1}}{\boldsymbol{{z}}}} \boldsymbol{{dz}},\:\boldsymbol{{then}}\:\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\left(\boldsymbol{{n}}+\mathrm{1}\right)!\boldsymbol{{I}}_{\boldsymbol{{n}}} =\boldsymbol{{I}}_{\mathrm{0}} +\boldsymbol{{e}}^{\frac{\mathrm{1}}{\boldsymbol{{z}}}} \left(\mathrm{1}\centerdot!\boldsymbol{{z}}^{\mathrm{2}} +\mathrm{2}\centerdot!\boldsymbol{{z}}^{\mathrm{3}} +\centerdot\centerdot\centerdot+\boldsymbol{{n}}!\centerdot\boldsymbol{{z}}^{\boldsymbol{{n}}+\mathrm{1}} \right) \\ $$$$ \\ $$…

Hard-integral-determinant-a-b-c-f-g-h-j-k-l-dl-dk-dj-dh-dg-df-dc-db-da-

Question Number 202418 by MathematicalUser2357 last updated on 26/Dec/23 $$\mathrm{Hard}\:\mathrm{integral} \\ $$$$\int\int\int\int\int\int\int\int\int\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{f}}&{{g}}&{{h}}\\{{j}}&{{k}}&{{l}}\end{vmatrix}{dl}\:{dk}\:{dj}\:{dh}\:{dg}\:{df}\:{dc}\:{db}\:{da}= \\ $$ Answered by Frix last updated on 26/Dec/23 $$\mathrm{Not}\:\mathrm{hard}\:\mathrm{at}\:\mathrm{all} \\ $$$$=\frac{{abcfghjkl}}{\mathrm{8}}\left({a}\left({gl}−{hk}\right)−{b}\left({fl}−{hj}\right)+{c}\left({fk}−{gj}\right)\right) \\…