2. [8 pts] Consider the region R enclosed by the graphs of functions f(x) = 2...
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...
Find the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the \(x\)-axis.Hint: You will need to evaluate two integrals. (Assume \(x>0 .\) )\(y=\frac{1}{x}, y=x_{r}\) and \(y=3 x\)By computing the volume of the solid obtained by revolving the region under the semicircle \(y=\sqrt{r^{2}-x^{2}}\) from \(x=-r\) to \(x=r\) about the \(x\)-axis, show that the volume of a sphere of radius \(r\) is \(\frac{4}{3} \pi r^{3}\), cublc units. (Do this by setting up the...
10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and x = 3. Find the volume of the solid generated by revolving this region around the axes given below. (Use the method of your choice.) Set up an INTEGRAL and then evaluate it using your calculator. a.) About the x-axis b.) About the y-axis c.) About the line x = 4
2/6 2" (10%) (a) Sketch the graphs of the two functions y=z(4-z) and y=z and mark the finite region (R) enclosed between them. (Identify (R) carefully!) (b) Let W be the volume of the solid of revolution obtained by revolving the above region (R) around the y-axis. (i) Use the shell method to write down the integral for W. (No need to evaluate the integral.) (ii) Repeat part(i) by using the disk method.
2/6 2" (10%) (a) Sketch the graphs...
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...
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...
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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...
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...
DRAW A SKETCH AND SHOW ALL WORK ROUND ANSWER TO HUNDREDS
Set up an integral that calculates the volume of the solid formed when revolving the region about the x-axis y 3 sin(2x) and y-XA28x -8
Set up an integral that calculates the volume of the solid formed when revolving the region about the x-axis y 3 sin(2x) and y-XA28x -8
Let R be the region bounded by the following curves. Use the disk method to find the volume of the solid generated by revolving the shaded region shown to the right about the x-axis. y=3-2x, y=0, x=0 Set up the integral that gives the volume of the solid using the disk method. Use increasing limits of integration