Question

In: Math

If R is the region bounded by the functions f(x)=x+4 and g(x)=−0.5x−1 over the interval [−2,0],...

If R is the region bounded by the functions f(x)=x+4 and g(x)=−0.5x−1 over the interval [−2,0], find the area of the region R as shown in the image.

Solutions

Expert Solution


Related Solutions

let R be a region bounded by x = 0 and x =1 and y =...
let R be a region bounded by x = 0 and x =1 and y = 0 and y = 1. Suppose the density is given by 1/y+1.Notice that R is denser near the x axis. As a result we might expect the centre of mass to be below the geometric center(1/2,1/2). Also since the density does not depend on x we do expect moment of inertia about the x axis to be 1/2. verify the moment of inertia about...
Integral Let f:[a,b]→R and g:[a,b]→R be two bounded functions. Suppose f≤g on [a,b]. Use the information...
Integral Let f:[a,b]→R and g:[a,b]→R be two bounded functions. Suppose f≤g on [a,b]. Use the information to prove thatL(f)≤L(g)andU(f)≤U(g). Information: g : [0, 1] —> R be defined by if x=0, g(x)=1; if x=m/n (m and n are positive integer with no common factor), g(x)=1/n; if x doesn't belong to rational number, g(x)=0 g is discontinuous at every rational number in[0,1]. g is Riemann integrable on [0,1] based on the fact that Suppose h:[a,b]→R is continuous everywhere except at a...
9) R is the region bounded by the curves ? = x^3 , y=2x+4 , And...
9) R is the region bounded by the curves ? = x^3 , y=2x+4 , And the y-axis. a) Find the area of the region. b) Set up the integral you would use to find the volume of a solid that has R as the base and square cross sections perpendicular to the x-axis.
Find the average value of f(x,y)= 4x+2y over region bounded by coordinate axis and lines x+y=4...
Find the average value of f(x,y)= 4x+2y over region bounded by coordinate axis and lines x+y=4 and x+y=8
Sketch the region and find the area completely enclosed by the functions f(x)=x2-1 and g(x)=1-x
Sketch the region and find the area completely enclosed by the functions f(x)=x2-1 and g(x)=1-x
Prove that if f is a bounded function on a bounded interval [a,b] and f is...
Prove that if f is a bounded function on a bounded interval [a,b] and f is continuous except at finitely many points in [a,b], then f is integrable on [a,b]. Hint: Use interval additivity, and an induction argument on the number of discontinuities.
5). Let f : [a,b] to R be bounded and f(x) > a > 0, for...
5). Let f : [a,b] to R be bounded and f(x) > a > 0, for all x in [a,b]. Show that if f is Riemann integrable on [a,b] then 1/f : [a,b] to R, (1/f) (x) = 1/f(x) is also Riemann integrable on [a,b].
1. Consider the region bounded by the graph of y^2 = r^2 −x^2 (a) When this...
1. Consider the region bounded by the graph of y^2 = r^2 −x^2 (a) When this region is rotated about the x-axis a sphere of radius r is generated. Use integration to find its volume V (b) Use integration to find the surface area of such a sphere 2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60] ( 3. Consider the graph of y = x^3 . Compute the surface area of...
Consider the region R, which is bounded by the curves  y=3x and x=y(4−y). (a) Set up, but...
Consider the region R, which is bounded by the curves  y=3x and x=y(4−y). (a) Set up, but DO NOT SOLVE, an integral to find the area of the region RR. (b) Set up, but DO NOT SOLVE, an integral to find the volume of the solid resulting from revolving the region RRaround the xx-axis. (c) Set up, but DO NOT SOLVE, an integral to find the volume of the solid resulting from revolving the region RRaround the line x=−5x=−5.
Calculate the integral of the function f (x, y, z) = xyz on the region bounded...
Calculate the integral of the function f (x, y, z) = xyz on the region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^ 2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT