A variable force, given by the 2-dimensional vector \( \vec{F}=\left(3 x^{2} \hat{i}+4 \hat{j}\r...

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A variable force, given by the 2-dimensional vector \( \vec{F}=\left(3 x^{2} \hat{i}+4 \hat{j}\right) \), acts on a particle. The force is in newton and \( x \) is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates \( (2,3) \) to \( (3,0) \) (The coordinates are in metres) [AMU (Med.) 2010]
(a) \( -7 \mathrm{~J} \)
(b) Zero
(c) \( +7 \mathrm{~J} \)
(d) \( +19 \mathrm{~J} \)
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