Along the path, y=x²/2 and dy=x dx. Therefore $\mathbf F\cdot d\mathbf r=x\,dx+5xy\,dy=[x+(5/2)x^4]dx$. Integrating from 0 to 2 gives $[x^2/2+x^5/2]_0^2=2+16=18$. The work depends on both force components along the curved path.
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