R is the region bounded above by the function f(x) = -x - 3 and below by the function g(x) = - 4x/3 - 7 over the interval [a, b] where a = -7 and b = 2. Represent R using the Desmos graph below. Submit your answer to this question by dragging the movable points so that the shaded region represents R.
Define R as the region that is bounded by the graph of the function f(x) = -2e^x/2, the x- axis, x = -1, and x = 0. Use the disk method to find the volume of the solid of revolution when R is rotated around the x-axis. Submit an exact answer in terms of π.
Define Q as the region that is bounded by the graph of the function g(y) = -2√y - 1, the y-axis, y = 3, and y = 5. Use the disk method to find the volume of the solid of revolution when Q is rotated around the y axis. Submit an exact answer in terms of π.
Define Q as the region that is bounded by the graph of the function g(y) = 2√y + 1, the y-axis, y = 1, and y = 3. Use the disk method to find the volume of the solid of revolution when Q is rotated around the y-axis.
Define R as the region that is bounded by the graph of the function f(x) = -3√3sin(x), the x-axis, x = π/6, and x = π. Use the disk method to find the volume of the solid of revolution when R is rotated around the x-axis. Submit an exact answer in terms of π.
Define R as the region that is bounded by the graph of the function f(x) = x^3/4 + 1, the x- axis, x = -1, and x = 2. Use the disk method to find the volume of the solid of revolution when R is rotated around the x axis. Submit an exact answer in terms of π.
Define Q as the region bounded by the functions u(y) = y^2/3 + 1 and v(y) = 1 between y = 3 and y = 4. Choose the integral below that describes the volume of the solid created by rotating Q around the line x = -1.
Q is the region bounded by the graph of v(y) = 5y, x = 4, and y = 0. Find the volume of the solid of revolution formed by revolving Q around the x-axis. Submit an exact answer in terms of π.
Define R as the region bounded by the graphs of f(x) = 3√x and g(x) = x^2/4 over the interval [1, 4]. Which of the following represents the volume of the solid of revolution formed by rotating R about the line x = -1?
Q is the region bounded by the graph of v(y) = 4y, x = 5, and y = 0. Find the volume of the solid of revolution formed by revolving Q around the x-axis. Submit an exact answer in terms of π.
Select the best method to find the volume of a solid of revolution generated by revolving the region bounded by the graph of y = -19x^2 + 19x and the x-axis around the line y = -15.
Select the best method to find the volume of a solid of revolution generated by revolving the region bounded by the graphs of y = 12x, y = -x + 2, and the x-axis around the x- axis.
Let f(x) = x^3/6 + 6 + 1/2x. Calculate the arc length of the graph of f(x) over the interval [2, 4]. Enter an exact answer.