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- 10.2 37)Find the area enclosed by the given parametric curve and the y-axis.Consider a curve represented by x2 + y2 = 4x.(a) Find the polar equation of f.(b) Set up the integral to find the area inside the curve f and outside r = 2.9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. (a) about the x-axis (b) about x = 4 please answer both a and b 1 to t to 2 x=4t, y=sqrt(t^2) but if you can only do one please do b
- Consider the parametric curve C that is defined byC: x=t^3, y=t^2+t, −1≤t≤3. c) Find a single integral whose value is the length of the curve C. Do not evaluate the integral.Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis from x = -2 to x = 2.The parametric curve below x=2t3, y=(4/2)t2, Integral to find its length from (0,0) to (16,8) a∫bf(t)dt a=? b=? f(t)=? So the length of the curve=?
- Find the area of the surface obtained by rotating the curve y = cos 2x, x is an element of [ 0, pi/6 ] about the x-axis.Consider the parametric equations below. x = t sin(t), y = t cos(t), 0 ≤ t ≤ ?/4 Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. ?/4 2π(tcost)√1+t2 dt 0 Use your calculator to find the surface area correct to four decimal places.Find the area of the surface generated by revolving the curve about the x axis y=√x, 0≤x≤2( Note: I used the s=integral 2pi√1+(dx/dy)^2 dx formula but got stuck on the u substitution section.)
- Consider the surface x^4+ 3xz + z^2+ cos( πxy ) = -2 and the point P0 ( -1, 1, 2) on that surface. Find an equation of (a) the tangent plane at P0 (b) the normal line to the surface at P0Consider the surface S shown in the graph, whose parametrization is given by: r (u, v) = (1 + 2v, 3uv, 4 - u2), where 0 ≤ u ≤ 2, 0 ≤ v ≤ 2 (see attached image with the graph) The surface differential, dS, is given by: (see image with possible answers)Find the area enclosed by one loop of this polar curve: r=3sqrt(cos2theta) from 0 to 2pi using the formula A=1/2 integral from 0 to 2pi (r)^2 for parametric curve.