VC4.7

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Since,r=xi+yj,dr=dxi+dyj\,

Therefore,\int _{{c}}F\cdot \,dr=\int _{{c}}(x^{2}y^{2}i+yj)\cdot (dxi+dyj)\,

=\int _{{c}}(x^{2}y^{2}dx+ydy)=\int _{{c}}x^{2}y^{2}dx+\int _{{c}}ydy\,

=\int _{{0}}^{{4}}x^{2}(4x)dx+\int _{{0}}^{{4}}ydy\, [Since y^{2}=4x\,]

=4[{\frac  {x^{4}}{4}}]_{{0}}^{{4}}+[{\frac  {y^{2}}{4}}]_{{0}}^{{4}}=256+8=264\,

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