Answer
Area
11-4ln4
With double integral find surface area when y=e", y = x, y = 4 and axis...
Find the area of the surface obtained by rotating the given curve about the x-axis. x = 20 cos (0), y = 20 sinº (0), 0 <O< 2 Preview
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...
2. (20 marks) (a) Calculate the surface area of the graph of f(x,y) = x + 20y over the region R= {(x,y) e R2:1 < x < 4,2 sy s 2x} in the xy-plane. OV (b) Integrate the function g(x, y, z) = x +y +z over the surface that is described as follows: x = 2u – v, y = v + 2u, z= v – u Here u € [0,20), v € [0,21].
5. Find the area of the surface obtained by revolving the curve y = sin(x), for 0 < x <TT, about the z-axis. [10] 6. Work out si 23 - 22 +7 +59 dx. [10] 23 x2 + x - 1
(1 point) Find the area of the surface obtained by rotating the curve y = yæ about y-axis for 1 < y < 2. Area:
9. Find the area of the surface by rotating the curve y2 -1 = x; 0 < x < 3 about the X-axis.
Consider the curve X = 42 y=ť, 0 <t<1 Setup the integral for the area of the surface obtained by rotating the curve about 27 (2+4 + 3t") dt [ 26 (28 + 3t) dt 2*t* 4 +01+ dt 27tº /2 + 3* dt [ 2013 (4+9t? dt
Find the integral that represents the length of the parametric curve defined by x = e' –t, y = 2e2, 0 <t < 1. Select one: o al. Vre! – 1° +1 dt ObſVe4 – 2e + 2 de o af Vibe' + e² - 2te + 1² de O d. ſ' vroeken? + e= nº di o of Vie + 1 di O !!! Vet – e' + 1 de o ' viel + 1) di on I' v2e...
5) (15 pts) Find the surface area of the surface generated by revolving the curvey 0 < x < 2; about the x-axis. (HINT: S.A 6) (15 pts) Find the length of the curve y = * - 4xfrom x = 1 to x = 2.
Suppose that f(2,y) = e* / on the domain D= {(2, y) 0 <y< 2,0 <I<y} HHHHHHH Then the double integral of f(2, y) over Dis f(x,y)d.cdy = Preview