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The value of int_(0)^(pi//2) sin^(4)x cos^(6)x dx, is |
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Answer» `(3pi)/(216)` `underset(0)overset(pi//2)int sin^(4)x cos^(6)x dx=(Gamma(5//2)Gamma(7//2))/(2Gamma(4+6+2)/(2))=(Gamma(5//2)Gamma(7//2))/(2Gamma6)` `rArr `underset(0)overset(pi//2)int sin^(4)x cos^(6)x dx=(((3)/(2)XX(1)/(2)xxGamma(1)/(2))((5)/(2)xx(3)/(2)xx(1)/(2)xxGamma(1)/(2)))/(2xx5!)=(3pi)/(512)` |
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