#2. Evaluate the integral of the function f(x, y) = xy + y² over the region R that is bounded by the x-axis, the line x = 4 and the curve y = √x. (a) Set up the integral using dA = dx dy. (b) Set up the integral using dA= dy dx. abunc Evaluate one of the two above and determine the numerical answer.

Q: Let f(x)=8/x^2 on the interval [1,4], For 1<a<4, Construct a rectangle from x=1 to x=a, with height…

A: Consider the graph for f(x) and draw a rectangle with height f(a) at point x = a. From the fig. find…

Q: MS and Confect The path C is a line segment of length 30 in the plane starting at (2, 2). For f(x,…

A:

Q: Find the absolute extrema of F(x,y)=3x^(2)+2y^(2)-4y over R, where R contains the boundaries, and R…

A:

Q: y=x² (-2,4) 0 (1,6) (2,4) 3y = 2x + 16 y=-2x+8 X

A:

Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the…

A:

Q: Find the area bounded by x=2y^2-4y+4 and x=y^2-2y+4.

A: To find the area between the curves x=2y2-4y+4, x=y2-2y+4.

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: y = vx from x = 0 to x = 4 and the x axis %3D

A: Given curves are  y=√x  x=0 to x=4 and the x- axis   We have to find the bounded region area .

Q: Find the area under the curve

A: To find area under the curve defined by the points (20,85), (15,83), (9,80) &amp; (7,78)We can use…

Q: Determine the area bounded by the curve: y=x^2-4x-5, y=0, between x=3 and x=6 y=1/4 (x^2-16), y=0,…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find the surface area generated by rotating x=4*sqrt(t), y= ((t^3)/3)+(1/2t^2), 1<=t<=3 around the…

A:

Q: 2(x + y)i + sin(y) 3. Find the line integral of Faround the perimeter of the rectangle with corners…

A:

Q: y = x - 15 x 10 y = x (4, 4) -6 -4 4 K-4,-4) - 10 - 20 20

A:

Q: Find the area of the region bounded by the curves y = x ^ 2 - 4x and x + y = 0

A: The equation of the curves are C1: y = x2-4xC2: x+y = 0 ⇒ y =-x  To determine: The area of the…

Q: Determine the area bounded by the curves y^2 = -4x and y = 2(x+2).

A:

Q: Find the points on the graph of the function f(x) = x^2 that are closest to (0, 2) in the xy-plane.…

A: Minimal distance

Q: Find the area of the region between the curve y = 3 - x² and the line y = 1 -x from x = 0 and x = 2.…

A: The region between the curve y=3-x2 and the line y=1-x from x=0 to x=2

Q: Find the area of ​​the region bounded by the curve x = 2y², the line 2y = x - 4 and line tangent to…

A: We need to find point of intersection to draw the graph and identify  region bounded by them ; Then…