Consider a solid whose base is the region bounded by the curves y = (−x^2) + 3 and y = 2x − 5, with cross-sections perpendicular to the y-axis that are squares. a) Sketch the base of this solid. b) Find a Riemann sum which approximates the volume of this solid. c) Write a definite integral that calculates this volume precisely. (Do not need to calculate the integral)
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...
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...
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...
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...
Let R be the region bounded by the y-axis and the graphs and as shown in the figure to the right. 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 4. and the graphs y = 1+x2 and y 4-2x 2x y = 4 as shown in the...
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.
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...
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 =