Question

Suppose C is a parametric curve given by x = sin 2t & y = - cos 2t for $t in [ -frac{pi}{4}, frac{pi}{4} ]$. Find a Cartesian equation for C Sketch the curve C, and label its starting point & terminal point as the parameter increases Is the orientation of C clockwise, or counterclockwise? Find an equation for the tangent line to C at the point corresponding to t = 0 Set up, and Evaluate the definite integral that gives the length of the curve C . Set up and Simplify, but DO NOT Evaluate, an integral for the 'area of the surface' obtained by rotating the curve, about the given axis. Sketch the base(s) of the surface. (i) $y = e^x$, $0 le x le 1$, about the x-axis (ii) $y = e^x$, $0 le x le ln 9$, about y-axis. Set up: S = Set up : S = Find the 'centroid' ($ar{x}$, $ar{y}$) of a lamina occupying the region between the x-axis and the curve y = $sqrt{x}$ for $0 le x le 1$.

          Suppose C is a parametric curve given by x = sin 2t & y = - cos 2t for $t in [ -frac{pi}{4}, frac{pi}{4} ]$.
Find a Cartesian equation for C
Sketch the curve C, and label its starting point & terminal point as the parameter increases
Is the orientation of C clockwise, or counterclockwise?
Find an equation for the tangent line to C at the point corresponding to t = 0
Set up, and Evaluate the definite integral that gives the length of the curve C
. Set up and Simplify, but DO NOT Evaluate, an integral for the 'area of the surface' obtained by
rotating the curve, about the given axis. Sketch the base(s) of the surface.
(i) $y = e^x$, $0 le x le 1$, about the x-axis (ii) $y = e^x$, $0 le x le ln 9$, about y-axis.
Set up: S = 
Set up : S = 
Find the 'centroid' ($ar{x}$, $ar{y}$) of a lamina occupying the region between the x-axis and the curve
y = $sqrt{x}$ for $0 le x le 1$.

$Suppose C is a parametric curve given by x = sin 2t y = - cos 2t for t in [ -fracpi4, fracpi4 ]. Find a Cartesian equation for C Sketch the curve C, and label its starting point terminal point as the parameter increases Is the orientation of C clockwise, or counterclockwise? Find an equation for the tangent line to C at the point corresponding to t = 0 Set up, and Evaluate the definite integral that gives the length of the curve C . Set up and Simplify, but DO NOT Evaluate, an integral for the 'area of the surface' obtained by rotating the curve, about the given axis. Sketch the base(s) of the surface. (i) y = e^x, 0 le x le 1, about the x-axis (ii) y = e^x, 0 le x le ln 9, about y-axis. Set up: S = Set up : S = Find the 'centroid' (arx, ary) of a lamina occupying the region between the x-axis and the curve y = sqrtx for 0 le x le 1.$

Added by Gregorio C.

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