we are given equations as
It is rotated about x=4 line
Firstly, we can draw graph
Bound is from 1 to 2
we can use shell method
now, we can set up integral
we can solve each integrals
and then combine them
............Answer
calculate volume The region R is bounded by the curves y = 22 +1 and y...
6. (a) (1 marks) Sketch the region bounded by the curves y = sin x, y = x+1, x = 0 and x = - 27. (b) (3 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 x = 27. (c) (3 marks) Use the method of washers to set up, but do not evaluate, an integral for the...
(1 point) Book Problem 9 Find the volume of the solid obtained by rotating the region bounded by the curves: 12 6 x ; about y 3x , y = = Volume (1 point) Book Problem 11 Find the volume of the solid obtained by rotating the region bounded by the curves: a2/4 22 ; about x =-3. y = x Volume:
(1 point) Book Problem 9 Find the volume of the solid obtained by rotating the region bounded by...
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. y= e- y0, x= -5, x-5 (a) About the x-axis (b) About y-1
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate...
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information is here.
5) Consider the region R bounded by the curves y x and y = 2x. Sketch the graphs, set up 2 formulas to find the volume of the solid obtained by rotating R (Slicing and Cylindrical shells), and evaluate these integrals using your calculator: -2 e) About the line x Slicing Method Cylindrical Shells Method f) About the line y 4. Slicing Method Cylindrical Shells Method g) About the line y- -1. Slicing Method Cylindrical Shells...
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...
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...
1.The region R is the region bounded by the functions y=x-3 and x=1+y^2. find the volume of the solid obtained by rotating the region R about the y axis. Please include a graph. 2.Find the volume of the solid obtained by rotating the region bounded by the graphs of y=x and y=sqrt(x) about the line x=2. Please include a graph
Region R is bounded by lines y=√x and y=x. A solid is obtained by rotating region R about line x=-1. Express the volume of this solid in the form if an integral.
7. Match the volume of the solid obtained by rotating the region bounded by the given curves about about the given axis to the corresponding integra 1, the region bounded by y-V , х--8 and the x-axis about the x-axis. 2. the region bounded by 8 and the r-axis about the y-axis. 3, the region bounded by y-V , y-2 and the y-axis about the x-axis. 4. the region bounded by V2 and the y-axis about the y-axis. 5, the...
2) The region R in the first quadrant of the xy-plane is bounded by the curves y=−3x^2+21x+54, x=0 and y=0. A solid S is formed by rotating R about the y-axis: the (exact) volume of S is = 3) The region R in the first quadrant of the xy-plane is bounded by the curves y=−2sin(x), x=π, x=2π and y=0. A solid S is formed by rotating R about the y-axis: the volume of S is = 4) The region bounded...