JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f\) be a real valued continuous function on \([0,1]\) and \(f(x)=x+\int\limits_{0}^{1}(x-t) f(t) d t\). Then which of the following points \(( x , y )\) lies on the curve \(y =f( x )\) ?
- A \((2,4)\)
- B \((1,2)\)
- C \((4,17)\)
- D \((6,8)\)
Answer & Solution
Correct Answer
(D) \((6,8)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left(1+\int\limits_{0}^{1} f(t) d t\right) x-\int\limits_{0}^{1} t f(t) d t\) \(f(x)=A x-B\) \(\dots(i)\) \(A=1+\int\limits_{0}^{1} f(t) d t=1+\int\limits_{0}^{1}(A t-B) d t\) \(\Rightarrow A=2(1-B)\) \(\dots(ii)\) Also…
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