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Q.) Find f(x) if f(x)=x+∫xy2+x2yƒ(y)dy. limits of integration - frm 0 to 1.
Dear navroze
f(x)=x+o∫1[xy2+x2yƒ(y)]dy
f(x) = x+ x/3 + x2o∫1yƒ(y)dy
o∫1yƒ(y)]dy it is a constant quantity let it is equal to c
so
f(x) = 4 x/3 + cx2
or f(y) = 4 y/3 + cy2
now c =o∫1yƒ(y)dy
put value of f(y)
c= o∫1y[4 y/3 + cy2]dy
c = 4/9 + c/4
3c/4 = 4/9
c =16/27
so f(x) = 4 x/3 + 16/27 x2
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