the volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to be solved using the circular ring method. The What is the expression corresponding to r? dh. Ormula for solving for the volume is given by V = "x (r.²-r ²) d a 4-2√√x = 2√5 - 1²/17 4-y
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- The volume of the solid generated by revolving the region bounded by x squared equals 4 y and y squared equals 4 x about y equals 4 is to be solved using the circular ring method. The formula for solving for the volume is given by V equals integral subscript a superscript b pi open parentheses r subscript o squared minus r subscript i squared close parentheses d h. What is the value of a? Choices: 0 4 2 1Find a formula involving integrals for a particular solution of D.Ey^‴-3y^″-y^'+3y=sectThe region in the first quadrant enclosed by the y-axis and the graphs of y=cos(x) and y=x is rotated about the x-axis. The volume of the solid generated is _______________. A. 0.877B. 1.520C. 0.484D. 1.831
- - Find by integration the area of the triangle having vertices at (5, 1), (1, 3), and (-1,-2). - Find by integration the area of the triangle having vertices at (3, 4), (2, 0), and (0, 1). - Find the area of the region bounded by the curve x³ x² + 2xy - y² = 0 and the line x = 4. (HINT: Solve the cubic equation for y in terms of x, and express y as two functions of x.) Find the area of the region bounded by the three curves y = x², x = y³, and x + y = 2. Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.Consider diffusion and reaction in a layer of soil. The problem is governed by the following equation and boundary conditions. Solve the problem using both boundary conditions at z=L using the characteristic equation in the form of exponentials and in the form of hyperbolic functions. Plot the solutions for D/kL = 0.1,1,and 10.A) Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the graph of f(x) = 11/x2 about the y-axis on the interval [1,3]. Please show all steps and round to the nearest hundredth. B) Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the graph of f(x) = 5 times the square root of (x - 8) about the y-axis on the interval [8,9]. Please show all steps and round to the nearest hundredth.
- How do you find the integral of cot^2(2pi*x)csc^6(2pi*x)dx? I've included some of my work below in two different blanks. I'm not sure what to pick for u in my integration by parts substitution, between u^3/3 or 2u since they both seem algebraic to me, although one looks obviously more complex. Overrall I know this work is at least half wrong.y''(x) + p(x) y'(x) + q(x) y(x) = 0 One of the solutions of the above eqation is given by y1(x) = sinh(2x). The solution of the wronskian of two indepentent is always constant. Find another solution of the equation indepentent from y1(x) for x>0 Please do in a readable manner, thanksI found a textbook example which intergrates an area function to find the volume of a solid of revolution bounded by the curve f(x) = (x-1)2 about the x-axis and the lines x=0 and x=2 using the disk method. The example shows a final solution change of intergration interval to x=1 and x=3 to arrive at the answer of 242pi/3 instead of the original interval x=0 and x=2? Would you show me step-wise how this was done or why it was necessary?
- calc 3 Evaluate the integral below, where E lies between the spheres x2 + y2 + z2 = 16 and x2 + y2 + z2 = 25 in the first octant.Find the volume. y = x6 ; y = 1 ; About y = 4 Apparently the answer is 35.7cubic units, but I'm not getting the same thing. Which method am I supposed to follow and how do you apply the y = 4 and y = 1 in the formula? Is y = 1 part of the bounds, too? Thoroughly confused on this problem. All explanations would be much appreciated. Thank you!Approximating the shaded area with the a) Trapezoidal rule and a step size of h=2 yields? .....in square units b) Trapezoidal rule and a step size of h=1 yields? .....in square units c) Romberg integration technique, with initial step size of h=2, yields? .....in square units