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Black Book Advanced Problems in MathematicsMathematicsIndefinite and Definite Integration

Given a function g , continuous everywhere such that g(1) = 5 and ₀^1 g(t) dt = 2 . If f(x) = 1 2 ₀^x (x - t)^2 g(t) dt , then find the value of f'''(1) + f''(1) .

Correct answer

7

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