Consider the region in the plane bounded by the curves y = x2 - 1, y = x + 1, and y = -x + 2 that contains the origin. 1.5 X 0.5 -1.5 -0.5 0 0.5 1!5 -0.5 We are trying to find the area of this region. If we integrate with respect to x, what is the minimum number of integrals we must use? If we integrate with respect to y, what is the minimum number of integrals we must use?The base of a solid is the region bounded in the plane by the curve y = -x + 3x and the x-axis. It's cross sections are squares that are perpendicular to the x-axis. The volume of this solid is computed by the integral Ad?. a The differential is O dx O dy The Area of each cross section is The limits of integration are a = b =The base of a solid is the region bounded in the plane by the curves y = va and x + y = 2 and the x-axis. It's cross sections are semicircles with diameters in the plane that are parallel to the x-axis. b The volume of this solid is computed by the integral Ad?. a The differential is O dy O dx The Area of each cross section is The limits of integration are a = b =The region in the plane bounded by the graphs y = x2 and x = y" is revolved around the line y = -2 To find the volume using the washer method, we will integrate with respect to Ox Oy To find the volume using the shell method, we will integrate with respect to Ox Oy The region in the plane bounded by the graphs y = x2 and x = y' is revolved around the line x = 2 To find the volume using the washer method, we will integrate with respect to Oy Ox To find the volume using the shell method, we will integrate with respect to Ox OyThe region in the plane bounded by the curves y = a and x = y is revolved around the line y = -2. Using the washer method, the outer radius of a washer is and the inner radius of a washer is Using the shell method, the height of the cylindrical shell is and the radius of the shell is (Use x or y for the variable, do not worry about the subscript i here)In order to compute the work necessary to pump water out of a tank, we approximate the actual shape of the tank of water with vertically-stacked slabs." Then for each slab we compute the work necessary to lift it out of the tank. In order to do this we multiply together which of the following quantities: O The price of the Calculus book The height of the water O Thickness of the Slab The value of the Stock market Density of Water O Distance the slab needs to be lifted O Cross-sectional Area of the slab O Acceleration of Gravity O The number of letters in your name