(15 points) The triangular region with vertices (0,0), (1,0) and (0,6) is rotated aboutthe line x= 3. Find the volume of the solid so generated.(Sketch the region and the solid obtained. Write down the name of the method used.)
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(15 points) The triangular region with vertices (0,0), (1,0) and (0,6) is rotated aboutthe line x=...
10. Consider the triangular region R with vertices (0.0) (a) (4 points) Sketch the triangular region R. Vertices (0.0), (0,2), and (4,0) 3/ lebel up, but do not evaluate, an integral for the volume of the solid obtained by rotating the triangular region R abo al (c) (4 points) Set up, but do not evaluate, an integral for the volume of the described solid. The base is the triangular region R. The cross-sections perpendicular to the r-axis are semi-circles with...
Integrate f(x,y)=x2 + y over the triangular region with vertices (0,0), (1,0), and (0,1). The value is (Type a simplified fraction.)
(15 pts) Find (2x - y) dA, where R is the triangular region with vertices (0,0), (1, 1), and (2, -1). Use the change of variables u = x - y and v = x + 2y.
plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1 point) Find the mass of the triangular region with vertices (0,0), (1, 0), and (0, 5), with density function ρ (x,y) = x2 +y. plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1...
find Ssey R R is a triangular region in x-y plane with vertices (-2, 2), (0,0), (2, 2)
5 ve 6. Soru Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
6. [10 points] Consider the function f(x) = 2 + cose over the interval (1,6), where I is measured in radians. Let S be the region that is bounded above by the graph of f(x), below by the 2-axis, on the left by the line = 1, and on the right by the line = 6. This question concerns the process of approximating, and exactly calculating, the volume of the solid that is obtained when S is rotated around the...
No48, 49, 50, 51 Please show me the details of solutions!! VOLUME In Questions 48-54 the region whose boundaries are given is rotated about the line indicated. Choose the alternative that gives the volume of the solid generated 48. y x" and y 4; about the line y -1. 49. y-3x x2 and y 0; about the x-axis. π(3(9x2 + x4) dr (A) We were unable to transcribe this image VOLUME In Questions 48-54 the region whose boundaries are given...
Find the volume of the solid obtained by revolving the indicated region about the given line. (Tip: Making a rough sketch of the region that’s being rotated is often useful.). The region is bounded by the curves x = √ sin y, x = 0, y = 0, and y = π and is rotated about the y -axis.
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. 8x3, y 0, x = 1 about x 2 V Sketch the region. 1아 6 WebAssign Plot 4 X 2.5 X 2 0 0.5 0.5 1,0 1,5 2i0 -0.5 0.5 1,0 1.5 2.5 + LC y 8 4 2 X X 210 210 -0.5 0.5 1,0 1.5 2,5 -0.5 0.5 1,0 1.5 2.5 Sketch the solid, and a typical...