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-- Mathematics - Section B1
Definite Integration
If $\int_0^xf(t)dt=x+\int_x^1t\,f(t)dt$ then the value of f(1) is:
1/2
0
1
-1/2
Differentiate w.r.t. x ⇒ f(x) – 0 = 1 + 0 – x f(x) × 1 ; Put x = 1 ⇒ f(1) = 1 – f(1) ⇒ f(1) = $\frac{1}{2}$