3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Fi...
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
Please help!! Thanks 1. Consider the function f(x) e a) Find the length of the curve given by the equation y - f(x), -1 3x<1. b) Let R be the region bounded by the graph of f(x) and the lines 1,1 and y-0. Find the area of R. c) Find the coordinates of the center of mass of R. d) Consider the solid obtained by rotation of R about the r-axis. Find its volume and surface area. 1. Consider the...
Show all work please. 1Find the area of the region bounded by the curves y 2x2 - 8x + 12 and y=-2 + 12. Find the volume when the area in question/qis revolved around the 3-axis. Find the volume when the area in question/grevolved around the y-axis. Va is revolved around the Ib Find the volume of the region formed when the area enclosed by y = x3 and y 2-axis. Consider only positive values of x. Find the volume...
1. Find the area between the graph x(t)=t^2, y(t)=t^2 + 2 and the x-axis when 0 is less than or equal to t and t is less than or equal to 4. 2. Find the surface area when the curve, x(t)=e^t + e^-t; y(t)=5 - 2t with 0 less than +t which is less than or equal to 3 and rotation about the x-axis. Please answer both problems if possible with work. Thank you in advance. 1. Find the area...
7 Consider the region bounded by y = sinx, y = cos x, x = 0, and x = Find the volume of the solid generated when the above region is revolved about 3-axis. Detailed drawing required. a b Find the volume of the solid generated when the above region is revolved about y -axis. Detailed drawing required. Hint: S = sin xdx = sin r - 100+, S roos edat = cos I+rsins + c.
The region bounded by the graphs of x-4y and y x 1. is revolved around y-axis. Find the volume of 2 - the solid generated in this manner. The region bounded by the graphs of x-4y and y x 1. is revolved around y-axis. Find the volume of 2 - the solid generated in this manner.
osts 1 = e' sint y=e' cost parametric equation of the curve part; a) find the length, b) Find the area of the surface formed by rotating it around the Ox- axis.
5. What is the derivative, and, of the parametric equation x = cost), y = et? A since -sin(t) C -sin(t). Det E There is no derivative. 6. Determine the integral which computes the volume of the solid formed by rotating the region bounded by y = 8-23, y = 0, and x = 0 about the x-axis. A B L=(8 – rød (** (3 – 20)? do +(8 – 23) dx 1 =18 # (8 – 2) da Ω...
between a y = et bounded by Find the area of the region of the region and by y = Sinx and x=0, x= 24 2