1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,
1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral. 2. Find the area of the region bounded by x=y^2+6, x=0 , y=-6, and y=7.
using the method of shells, set up, but don't evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1
1. Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 36x^2+25y^2=1. L= double integral R (4sin(144x^2+100y^2) dA. 2. Use the given
Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -3 I got the integral from 1 to 2.718 of pi(1)^2-pi(ln(x))^2 Is
The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write,
Use the shell method to set up, but do not evaluate, an integral representing the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4x-x^2 about the line x=6. I had the shell radius as
Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 7. I have to use the volume by disks method, but I'm confused