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Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations

Let F be the set of all continuous real valued functions which are solutions to f^2(x)=100+ ₀^x (f(t) f^ (t)-f(t)-f^ (t)-1 ) d t . Find the value of 1 |F| _ f(x) F |f(100)| .

Correct answer

100

Step-by-step solution

f(0)= 10 Differentiating both sides, we get array ll & (f(x)+1) _ rejected (f^ (x)+1 )=0 & f(x)=10-x or -10-x Hence, & 1 | ~F | _ f(x) F |f(100)|= 1 2 (90+110)=100 array

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