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The value (int_(0)^(pi//2) (sinx)^(sqrt2+1)dx)/(int_(0)^(pi//2)(sinx)^(sqrt2-1)dx) is - |
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Answer» `(sqrt2+1)/(sqrt2-1)` `I_(1)=((SINX)^(sqrt2)intsin"x dx")_(0)^(pi//2)-overset(pi//2)underset(0)int(sqrt2(sinx)^(sqrt2-1)COSX intsin"x dx")` `=-(cos x(sinx)^(sqrt2))_(0)^(pi//2)+sqrt2overset(pi//2)underset(0)int(sinx)^(sqrt2-1)(1-sin^(2)x)dx` `(I_(1))/(I_(2))=(sqrt2)/(1+sqrt2)xx((sqrt2-1))/((sqrt2-1))=2-sqrt2` |
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