1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus c) Use double integral to get the surface area of this torus. 1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the...
Ch.8 1. When the region R={(x, y) x 21,0 5 y 51/x is rotated around the x-axis, we get a solid famously known as Gabriel's Horn. (a) Show that R has infinite area (recall, R is the region BEFORE rotation). (b) Show that Gabriel's Horn has a finite volume. Hint: Use the disk method. (c) Show that Gabriel's Horn has infinite surface area. Hint: Use the comparison theorem for integrals on page 533 of your textbook. Note: For all parts,...
Integral Determine the shaded area enclosed by y 0 and the equation yr (0sxSI). 1 y=x 1 Double integral (Use polar coordinate) Find the volume of the solid bounded by the plane z-0 and the surface z r(r=x+ y,0Srsl). 1
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane. 4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos v)cos ui + (a + b cos v)sin uj + b sin vk, where a > b, 0 2 π, b > 0, and 0 2π u v Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos...
Help with question 2 1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density....
Need ONLY 2-3 with work shown Directions: In each problem (1)-(5), write a definite integral of a single variable. For problems marked [FTC], use the Fundamental Theorem of Calculus to evaluate the definite integral. Use a calculator utility for problems marked [Calculator Active]. Show intermediate steps, and box in your final result. « Submit a single team set of solutions on the answer sheets provided.» > (0) Region R is bounded by the curve y -x and the line y...
4. Use an appropriate iterated integral and coordinate system to find the volume of the solid. B) inside the graphs r-2 cos θ and r. 4 4. Use an appropriate iterated integral and coordinate system to find the volume of the solid. B) inside the graphs r-2 cos θ and r. 4
8. Use the shell method to set up and evaluate the integral y- 3x that gives the volume of the solid generated by revolving the plane region about the y-axis. a. 192R b. 384x C. 192x d. 384x e. 96x 7 9. Set up and evaluate the definite integral for the area of the surface formed by revolving graph of y-9-2 about the y-axis. Round your answer to three decimal places. 8. Use the shell method to set up and...
can i get answer for all thses questions pllllleeeease Evaluate the double integral by first identifying it as the volume of a solid. STS- (7 - x) DA, R = {(x,y) 10 sxs 7,0 y s 6} 144 x Need Help? Read It Talk to a Tutor Calculate the iterated integral. 12 Sex + 3y dx dy 4397. 107 Х Need Help? Read It Talk to a Tutor 6. [-/1 Points) DETAILS SESSCALCET2 12.1.035. MY NOTES Find the volume of...