Standard problems of calculus.

Calculus Level 4

We have a continous and differentiable curve f(x)=y passing through (1,1) satisfying the property that the tangent drawn to the curve at the point (x,f(x)) intersects the x-axis at the point (2x,0).

Find the value of $$\int _{ 1 }^{ 2 }{ f(x)dx }$$

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