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If `I_(1)=int_(0)^(1)(1-(1-x^(3))^(sqrt(2)))^(sqrt(3)) x^(2)dx` and `I_(2)(1-(1-x^(3))^(sqrt(2)))^(sqrt(3)+1).x^(2)dx`. Then `((I_(1))/(I_(2))-(sqrt(3)-1)/(2sqrt(2))+0.2)/10` is equal to _________ |
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Answer» Correct Answer - `00000.12` Let `1-x^(3)=t` `3l_(1)=int_(0)^(1)(1-t^(sqrt(2)))^(sqrt(3)) dt` and `3l_(2)=int_(0)^(1)(1-t^(sqrt(2)))^(sqrt(3)+1).1.dt` `=int_(0)^(1)(sqrt(3)+1)sqrt(2)(1-t^(sqrt(2)))^(sqrt(3))(1-t^(sqrt(2))-1)dt` (Using integration by parts) `3l_(2)=-(sqrt(3)+1)sqrt(2).3l_(2)+(sqrt(3)+1)sqrt(2).3l_(1)` So, `(l_(1))/(l_(2))-(sqrt(3)-1)/(2sqrt(2))+0.2=1+(sqrt(3)-1)/(sqrt(2))-(sqrt(3)-1)/(2sqrt(2))+0.2=1.2` |
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