Set, Relation and FunctionHard

Question

Let f(x) be a function satisfying f′(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2. Then the value of the integral f(x) g(x) dx, is

Options

A.
B.
C.
D.

Solution

f(x) [x2 - f(x)] dx
solving this by putting f′(x) = f(x).
Hence, (B) is the correct answer.

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