JEE Mains · Maths · STD 12 - 7.2 definite integral
If \( f(x) \) satisfies the relation \( f(x)=e^{x}+\int_{0}^{1}(y+xe^{x})f(y)dy, \) then \( e + f(0) \) is equal to ___ .
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(f ( x )= e ^{ x }+\int_0^1 yf ( y ) dy + xe ^{ x } \int_0^1 f ( y ) dy\) \(f ( x )= e ^{ x }+ A + Bxe ^{ x } \) \(A =\int_0^1 yf ( y ) dy =\int_0^1 y \left( A + e ^{ y }+ By e ^{ y }\right) dy\) \(A =\frac{ A }{2}+(0-(-1))+ B ( e -1)\) \(\frac{ A }{2}+ B (1- e )=1\)…
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