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 volu...
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...
2.6 Set up the integral expression for the average value of the distance to the origin of points in the triangular region R with vertices (0, 0), (a, 0) and (0, b) for positive constants a, b Do not compute the integral 2.7 Compute the average value of the squared distance to the origin of points in the triangular region R with vertices (0, 0), (4, 0) and (0, 2) tor to evaluate th resulting (single) integral to two decimals....
1 point) Book Problem 1 (x) x5 x-5 g(x> 0.8a2 8 Set up an integral to find the area A of the region enclosed between f(x) and g(x) -5 to x = 5, and then evaluate it. = x from T= da A - (1 point) Book Problem 39 The base of a certain solid is an elliptical region with boundary curve 4x2 25y2 100. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. A(x)...
need it asap please 18) 8. The region is bounded by y = 2 - r- and y = r. (a) (2 marks) Sketch the region. (b) (6 marks) Find the area of the region. (c) (5 marks) Use the method of cylindrical shells to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line r = -3. (d) (5 marks) Use the disk or washer method to...
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...
4. The region bounded by y = r - 1+1 and x = 2y – 1 is shown in the figure. y= (x-1 +1 x = 2y - 1 (5,3) (1,1) (a) (6 points) Set up but DO NOT EVALUATE the integral(s) that measure(s) the volume of the solid obtained by rotating the region about the x-axis. (b) (6 points) Set up but DO NOT EVALUATE the integral(s) that measure(s) the volume of the solid obtained by rotating the region...
Problem 3 6 pts] The region R bounded by y V, y 0, and 4 is revolved about the line y3 Calculate the volume of the solid using the washer method and simplify your final answer. -3 Problem 4: 8 pts] The region R is boud by y2 and y 8- 2 I. Set up, but do not evaluate, an integral or sum of integrals that would give the volume of the solid of revolution formed when R is revolved...
The following integral was used to compute the area of a region D using the horizontal slicing ( [~-)) - (a) Sketch and shade the region D. Label all the intersection points. (b) Set up the definite integral to evaluate the area of the same region D using the vertical slicing. Do not evaluate the integral. (c) Draw a typical washer or a cylindrical shell and set up the definite integral to evaluate the volume of the solid by rotating...
The following integral was used to compute the area of a region D using the horizontal slicing dy (a) Sketch and shade the region D. Label all the intersection points. (b) Set up the definite integral to evaluate the area of the same region D using the vertical slicing. Do not evaluate the integral. (c) Draw a typical washer or a cylindrical shell and set up the definite integral to evaluate the volume of the solid by rotating the region...
The following integral was used to compute the area of a region D using the horizontal slicing 4 - ) - 3] du (a) Sketch and shade the region D. Label all the intersection points. (b) Set up the definite integral to evaluate the area of the same region D using the vertical slicing. Do not evaluate the integral. (c) Draw a typical washer or a cylindrical shell and set up the definite integral to evaluate the volume of the...