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- 1. Compute E yz dV , where E is the region above z 0, below z y, and inside x 2 y 2 4If we rotate the region under the curve y = 8 between x = 2 and x = 3 about the x-axis, what answer should the Shell Method give us?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)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)Suppose that 0< c < π/2 . For what value of is thearea of the region enclosed by the curves y= cos x,y= cos (x -c), and x=0 equal to the area of the regionenclosed by the curves y= cos(x- c) , x =π , and y=0 ?Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid formed by revolving A around the line x= −2.
- Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices (0,0,0),(7,0,0),(0,7,0),(0,0,7).1. Consider the region bounded by y = x and y =√x, shown below.xyFind the volume of the solid obtained by rotating this region about the line x = 3.Answer question 4 4. Region bounded by y = x 2, x=0 and y=15, rotated about the y-axis
- Sketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.Sketch the region enclosed by y=e^3x ,y=e^8x, and x=1. Decide whether to integrate with respect to x or y, and then find the area of the region.3.1 Use the Cauchy integral formulas to evaluate the ∮c eizcos z/ z2(2z -3π) dz, where C is the region covered by circle |z - 2| = 3.