3.2. Find the volume of the solid obtained by revolving the region bounded by \[ y=\frac{x}{2} \text { and } x=2 \text {, } \] about the line \( y=2 \). Draw the sketch graph. 3.3. Find the arc length of the graph on the interval \( [1,2] \). 3.4. Find the area of the surface formed by revolving the graph of \[ f(x)=x^{3}, \] on the interval \( [0,1] \) about the \( x \)-axis.

Evaluate the line integral. \( \int_{C} 5 z d s \), where \( C \) is the line segment from \( (5,0,1) \) to \( (6,-6,6) \) \( \int_{C} 5 z d s=\square \)

Compute the work done by the force field \( F=\langle y, 0, z\rangle \) along the triangle from \( (0,0,0) \) to \( (2,3,4) \) then to \( (2,3,0) \) and then back to \( (0,0,0) \). \( W=\square \)

Compute the divergence of \( F(x, y)=1.2 x i+1.75 y j \) \( \operatorname{div} F=\square \)

Label each expression as a scalar quantity, a vector quantity or undefined, if \( f \) is a scalar function and \( F \) is a vector field. \( \nabla \times(\nabla f) \) scalar vector

52. \( \star \sum_{n=1}^{\infty} \sqrt{n}(\sin n)\left(\sin \frac{1}{n}\right)^{2} \)