Ta có : \(h\left(x\right)=1+2018\int\limits^x_0f\left(t\right)dt=f^2\left(x\right)\)
\(\Rightarrow h'\left(x\right)=2018f\left(x\right)=2f\left(x\right).f'\left(x\right)\)
\(\Rightarrow f'\left(x\right)=\dfrac{2018}{2}=1009\)
\(\Rightarrow f\left(x\right)=\int\limits f'\left(x\right)dx=1009x+C\)
\(\Rightarrow h\left(x\right)=\left(1009x+C\right)^2\)
mà \(h\left(0\right)=1\)
\(\Rightarrow C=1\)
\(\Rightarrow\int\limits^1_0f\left(x\right)dx=\int\limits^1_0\left(1009x+1\right)dx=\dfrac{1009}{2}x^2+x|^1_0=\dfrac{1009}{2}+1=\dfrac{1011}{2}\)
\(\Rightarrow\) Chọn D
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