The area shown shaded is in a flow where the velocity field is given by \(\vec{V}=a x \hat{i}+b y \hat{j}+c \hat{k} ; a=b=2 \mathrm{~s}^{-1}\) and \(c=1 \mathrm{~m} / \mathrm{s}\). Write a vector expression for an element of the shaded area. Evaluate the integrals \(\int_{A} \vec{V} \cdot d A\) and \(\int_{A} \vec{V}(\vec{V} \cdot d \vec{A})\) over the shaded area.

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3 m N x 4m 5 m P4.11