Question 1 (2 points) ✓ Saved The base of a solid, s, is the region enclosed...
Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 4 − 2x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.
For each problem, find the volume of the solid that results when the region enclosed by the curves is revolved about the given axis. For each problem, find the volume of the solid that results when the region enclosed by the curves is revolved about the the given axis. 13) y= Vx+2, y=2, x=1 Axis: y = 2 26) *= y2 - 1, x= Vy-1 Axis: x = 2 For each problem, find the volume of the specified solid. 2)...
(1) Consider the solid S described below. The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 3). Cross-sections perpendicular to the y-axis are equilateral triangles. Find the volume V of this solid. V = (2)Consider the solid S described below. The base of S is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross-sections perpendicular to the x-axis are squares. Find the volume V of this solid. V =...
The base of a solid is the region bounded by lines y = -1 + 2, x = 0 and y = 0. Cross-sections perpendicular to the z-axis are squares with a side in the base. Find the volume of the solid. Sketch the region.
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
1) Problem 12 The area of the region bounded by the parabola x y-3) and the line y x is Problem 13 The base of a solid S is the parabolic region [(x.y):x s y S 1). Cross-sections perpendicular the y-axis are squares. Find the volume of the solid S 1) Problem 12 The area of the region bounded by the parabola x y-3) and the line y x is Problem 13 The base of a solid S is the...
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...
Problem 2 (1) Find the area enclosed by the curves y 2 and y-4z-z2 (2) Find the volume of the solid whose base is the triangular region with vertices(0, 0), (2, 0), and (0,1). Cross-sections perpendicular to the y-axis semicircles. are (3) Find the volume of the solid by rotating the region bounded by y=1-z2 and y-0 about the r-axis. 2-z2. Find the volume (4) Let R be the region bounded by y--x2 and y of the solid obtained by...
(1 point) Find the volume of the solid whose base is the region in the first quadrant bounded by y=x?, y=1, and the y-axis and whose cross-sections perpendicular to the x axis are squares. Volume =
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...