The region R is the base of a solid. Find the volume of this solid, assuming that each cross section perpendicular to the x-axis is:
a) a square.
b) an equilateral triangle.
Let R be the region bounded by the y-axis and the graphs and as shown in...
Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above. a) Find the area of R. b) Region R is the base of a solid. For the solid, each cross-section perpendicular to the x-axis is a right isosceles triangle whose leg falls in the region. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. c)...
3. Let R be the region bounded by the graphs of y4, and the -axis Find the volume of the solid that has R as its base if every cross section by a plane perpendicular to the x-axis is a square. Please include a picture of the base and the slice and write the area and volume of the slice. 5.333 2 3 3. Let R be the region bounded by the graphs of y4, and the -axis Find the...
5. Let R be the region bounded by the graph of, y Inr + 1) the line y 3, and the line x - 1. (a)Sketch and then find the area of R (b) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. (c) Another solid whose base is also the region R. For this solid, each cross section perpendicular to the x-axis is a Semi-circle...
cannot figure out how to write the integrals for this problem #2 1. If glx) -2x and fx) - , find the area of the region enclosed by the two graphs. Show a work for full credit. (4 pts) 2. A:12-80% 3 3 2 Let fix)-. Let R be the region in the first quadrant bounded by the gruph of y - f(x) and the vertical line x # l, as shown in the figure above. (a) Write but do...
Find the volume of the solid generated by revolving the region R bounded by the graphs of the given equations about the y-axis. 17)x= x=0, between y=- 4 and y = 4 17) 18) bounded by the circle x2 + y2 = 16, by the line x = 4, and by the line y = 4 18) Find the volume of the solid generated by revolving the region about the given line. 19) The region in the first quadrant bounded...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
8. Consider the region bounded by the y = x2 - 2x + 1 and y = 1 + 2x - x? Find the area of the region. a. b. Find the volume of the solid when the region is rotated about the x-axis. c. Find the volume of the solid when the region is rotated about the y-axis. d. Find the volume of the solid when the region is rotated about the line x = 5. e. If the...
4. Let R be the region bounded by x = y2 and x = 4. see picture. Find the volume of the solid of base R, whose cross-sections are equilateral triangles perpen- dicular to the x-axis. 2 y R х 1 2 3 -1 -2
I'm getting it wrong for some reason and it's literally right?! Can someone explain to me what is going on Let S be the solid with flat base, whose base is the region in the z y plane defined by the curves y - e,y--1,0and a-1, and whose cross sections perpendicular to the x axis are equilateral triangles with bases that sit in the r y plane a) Find the area A() of the cross-section of S given by the...
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...