A solid has a cross section perpendicular to the x-axis, which is a square with side length \(y\). If the function \(y = 2x + 1\) represents the upper boundary of the solid from \(x=0\) to \(x=3\), find its volume.

If \( f(x)=\frac{1}{3} x^{3}+c x^{2}+a x+5 \) has alocal mintmum value at \( x=1 \). what is the value of \( a \) and \( c \) ?

b) \( y=\frac{x-1}{x^{2}+2 x+3} \)

Find the volume of the solid formed by rotating the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 3 \) about the y-axis.

If \( f(x)=\frac{1}{3} x^{3}+c x^{2}+a x+5 \) has alocal manamum value at \( x=1 \), + What is the value of a \( f c \) ?

Evaluate the triple integral. \[ \iiint_{G} x y z d V \] where \( G \) is the solid in the first octant that is bounded by the parabolic cylinder \( z=3-x^{2} \) and the planes \( z=0, y=x \) and \( y=0 \).