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Question Number 54765 by peter frank last updated on 10/Feb/19

Answered by tanmay.chaudhury50@gmail.com last updated on 10/Feb/19

$$\frac{1}{2}\times 2{\int }_0^{\frac{\pi }{2}}{sin}^{2\times 24-1}{xcos}^{2\times 27-1}xdx$$$$formula2{\int }_0^{\frac{\pi }{2}}{sin}^{2p-1}{xcos}^{2q-1}xdx$$$$=\frac{\lceil \left(p\right)\lceil \left(q\right)}{\lceil (p+q)}$$$$soansis=\frac{1}{2}\times \frac{\lceil \left(24\right)\times \lceil \left(27\right)}{\lceil \left(51\right)}=\frac{1}{2}\times \frac{23!26!}{50!}$$$$firmulagammafunction\to \lceil (n+1)=n!\left(factirial\right)$$$$$$$$$$

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