VC4.7

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

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

=\int_{c}(x^2y^2dx+ydy)=\int_{c}x^2y^2dx+\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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