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Q.) Find f(x) if f(x)=x+∫xy 2 +x 2 yƒ(y)dy. limits of integration - frm 0 to 1.

Q.) Find f(x) if f(x)=x+∫xy2+x2yƒ(y)dy. limits of integration - frm 0 to 1.

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1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear navroze

f(x)=x+o1[xy2+x2yƒ(y)]dy

f(x) = x+ x/3  + x2o1yƒ(y)dy

 o1yƒ(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 =o1yƒ(y)dy

put value of f(y)

  c= o1y[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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