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Let S(alpha)={(x,y):y^(2) le x, 0 le x le alpha} and A(alpha)is area of the regions S(alpha). " If for " lambda, 0 lt lambda lt 4, A(lambda): A(4)=2:5, then lambda equals |
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Answer» `2((4)/(25))^((1)/(3))`  Clearly, `A(lambda)=2int_(0)^(lambda)sqrt(x)dx=2[(x^(3//2))/(3//2)]_(0)^(lambda)=(4)/(3)lambda^(3//2)` Since, `(A(lambda))/(A(4))=(2)/(5),(0 lt lambda lt 4)` `RARR (lambda^(3//2))/(4^(3//2))=(2)/(5) rArr ((lambda)/(4))^(3)=((2)/(5))^(2)` `rArr (lambda)/(4)=((4)/(25))^(1//3) rArr lambda=4((4)/(25))^(1//3)` |
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