1.

Let f:[0,2]→R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1. Let F(x)=x2∫0f(√t) dtfor x∈[0,2]. If F′(x)=f′(x) for all x∈(0,2), then F(2) equals

Answer»

Let f:[0,2]→R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1. Let

F(x)=x2∫0f(√t) dt

for x∈[0,2]. If F′(x)=f′(x) for all x∈(0,2), then F(2) equals


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