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Question Number 97721 by Power last updated on 09/Jun/20

Commented by mr W last updated on 09/Jun/20

Commented by smridha last updated on 09/Jun/20

$$thisisnot\mathit{t}\mathit{h}\mathit{e}\mathit{s}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}!!!$$

Commented by mr W last updated on 09/Jun/20

$$wow,redboldtextwiththree$$$$exclamationmarks!$$

Answered by smridha last updated on 09/Jun/20

$$\mathit{l}\mathit{e}\mathit{t}\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)=\mathit{u}\mathit{s}\mathit{o}$$$$\int {(1-{\mathit{u}}^2)}^{\frac{(\mathit{m}-1)}{2}}{\mathit{u}}^{\mathit{n}}\mathit{d}\mathit{u}$$$$=\int \underset{\mathit{r}=0}{\sum ^{\frac{(m-1)}{2}}}{\stackrel{\frac{(\mathit{m}-1)}{2}}{C}}_{\mathit{r}}{\left(1\right)}^{\mathit{r}-\frac{(\mathit{m}-1)}{2}}.{(-1)}^{\mathit{r}}{\mathit{u}}^{2\mathit{r}}{\mathit{u}}^{\mathit{n}}\mathit{d}\mathit{u}$$$$=\underset{\mathit{r}=0}{\sum ^{\frac{(\mathit{m}-1)}{2}}}{(-1)}^{\mathit{r}}.{\stackrel{\frac{(\mathit{m}-1)}{2}}{\mathit{C}}}_{\mathit{r}}\frac{{\left(\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)\right)}^{2\mathit{r}+\mathit{n}+1}}{(2\mathit{r}+\mathit{n}+1)}+\mathit{g}$$

Commented by Power last updated on 09/Jun/20

$$\mathrm{Brilliant}!\mathrm{I}\mathrm{would}\mathrm{be}\mathrm{glad}\mathrm{if}\mathrm{you}\mathrm{give}\mathrm{me}\mathrm{an}\mathrm{idea}$$

Commented by smridha last updated on 09/Jun/20

$$\mathit{a}\mathit{b}\mathit{o}\mathit{u}\mathit{t}\mathit{w}\mathit{h}\mathit{a}\mathit{t}?$$

Commented by Power last updated on 09/Jun/20

$$\mathrm{solution}$$

Commented by smridha last updated on 09/Jun/20

$$at\mathit{f}\mathit{i}\mathit{r}\mathit{s}\mathit{t}\mathit{I}\mathit{B}i\mathit{n}\mathit{o}\mathit{m}\mathit{i}\mathit{a}\mathit{l}\mathit{l}\mathit{y}\mathit{e}\mathit{x}\mathit{p}\mathit{a}\mathit{n}\mathit{d}$$$${(1-{\mathit{u}}^2)}^{\frac{(\mathit{m}-1)}{2}}\mathit{t}\mathit{h}\mathit{e}\mathit{n}\mathit{i}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{c}\mathit{h}\mathit{a}\mathit{n}\mathit{g}\mathit{e}\mathit{d}$$$$\mathit{s}\mathit{u}\mathit{m}\mathit{m}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{a}\mathit{n}\mathit{d}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{g}\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$\mathit{b}\mathit{e}\mathit{c}\mathit{a}\mathit{u}\mathit{s}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{g}\mathit{r}\mathit{a}\mathit{n}\mathit{d}\mathit{f}\mathit{u}\mathit{n}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$\mathit{i}\mathit{s}\mathit{u}\mathit{n}\mathit{i}\mathit{f}\mathit{o}\mathit{r}\mathit{m}\mathit{l}\mathit{y}\mathit{c}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{g}\mathit{e}\mathit{n}\mathit{t}....$$$$\mathit{a}\mathit{n}\mathit{d}\mathit{y}\mathit{o}\mathit{u}\mathit{a}\mathit{l}\mathit{s}\mathit{o}\mathit{c}\mathit{h}\mathit{e}\mathit{c}\mathit{k}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{b}\mathit{y}\mathit{p}\mathit{u}\mathit{t}\mathit{t}\mathit{i}\mathit{n}\mathit{g}$$$$\mathit{t}\mathit{h}\mathit{e}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{o}\mathit{f}\mathit{m}\mathit{a}\mathit{n}\mathit{d}\mathit{n}\mathit{a}\mathit{s}\mathit{y}\mathit{o}\mathit{u}\mathit{r}\mathit{w}\mathit{i}\mathit{s}\mathit{h}$$

Commented by Power last updated on 09/Jun/20

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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