5. Find the area of the surface obtained by rotating the curve y=Vx on the interval [0,1] around the y-axis. 6. Evaluate the integral dx (x+1)
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.
3. (6 points) Consider the curve y = 2 - 2.22 restricted to the first quadrant. (a) Set up a definite integral that gives the length of this curve. Do NOT evaluate the integral (b) Set up a definite integral that gives the surface area of the solid generated by rotating the curve about the x-axis. Do NOT evaluate the integral.
Consider the following curve on the given interval. a. Write the integral that gives the area of the surface generated when the curve is revolved around the x-axis. b. Use a calculator or software to approximate the surface area. f(x) = x® on [0,1] 2 a. Write the integral. 1 S= S 26 (29) 1+ (2x)? 0 b. Find the surface area. S៖ (Type an integer or decimal rounded to three decimal places as needed.)
Let S be the ‘football’ surface formed by rotating the curve y = 0, x = cos z for z ∈ [−π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area. Please answer in full With full instructions. Let S be the 'football, surface formed by rotating the curve y = 0, x-cosz for-E-π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area 3 Let S be the 'football, surface...
problem 3 pls Problem 3. Consider the curve {> 1, y = 1/x}. Compute the length of the part of this curve lying to the left of the line x = a for any a > 1. Show that the length of the whole curve is thus infinite. Compute the area of the surface obtained by rotating this curve about about the x axis by computing the corresponding improper integral; it should be infinite. What is the area of the...
1. The area between the part of the curve-6x 8 above the x-axis and the x-axis itself is 2. The area below y 4x -x and above y 3 (for1 xS 3) is revolved around the x-axis. 3. The areas between the following portions of curves and the x-axis are revolved around the revolved by an angle 2π around the x-axis. Find the volume swept out. Find the volume swept out. y-axis. Find the volume swept out. (a) y- betweenx...
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
Find the surface area of the solid of revolution obtained by rotating the curve x=(1/12)(y^2+8)^(3/2) from ?=2 to ?=5 about the x-axis: (1 point) Find the surface area of the solid of revolution obtained by rotating the curve X= +8)3/2 from y = 2 to y = 5 about the x-axis:
4. [8 points] What is the volume of the solid formed by taking the the area between y = 4- 4x and the x-axis on the interval [0,1], and rotating it about x = 2? Fill in the following blanks to show your work and final answer. Setup but do not solve the definite integral. Volume of slice: Riemann Sum: Sketch of picture: Definite Integral: