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- In the given question find b such that the line y b divides the region bounded by the graphs of the equations into two regions of equal area y = 9 - lx l ,y = 017. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the x-axis (d) y = 4Sketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.
- integrate ƒ over the given region. ƒ(x, y) = x2 + y2 over the triangular region with vertices (0, 0), (1, 0), and (0, 1)Find the value of c > 0 such that the regionbounded by the cubic y = x(x - c)2 and the x-axis on the interval[0, c] has area 1.1. Compute E yz dV , where E is the region above z 0, below z y, and inside x 2 y 2 4
- if d is the region in the first octant between the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=25 then. the rest of question in the following imageGiven : The region is bounded by the curve y=4x-x^2, y=4 and the y-axisProblem :The intersection of the bounding curves are shown below, find a + b + c.1)Sketch the solid obtained by rotating the region bound byy=2√x and y=x, about the line x =−2. 2)Write the expression for the area of a representative washer 3)Set up and solve the definite integral used to calculate the volume of the solid in (1)
- 1. Estimate the volume of the solid that lies below the surface z = xy and above the rectangle R = {(x,y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ 4}.(a) using Riemann sum with m = 3, n = 2, and take the sample point to be the upper the right corner of each square(b) using midpoint rule with the same values of m and n in problem (a).1) Consider the region in the xy-plane that is bounded by y = 3 x^2 and y=3x for x ≥ 0. Revolve this region about the y-axis Super quickly so that your eyes glaze over and it eventually looks like a solid object at one point. What would the volume of this solid be? Make sure to include every step.determine by inspection at least twosolutions of the given first-order IV .15. y- 3y2/3, y(0) 016. xy- 2y, y(0) 0