1Which of the following integrals computes the volume of the

1.Which of the following integrals computes the volume of the solid formed by revolving the region bounded by the graph of y = Ln(x), the x-axis, and the line x = 3 about the line x = 3?

3.

Use the trapezoidal rule with n = 4 to approximate the area bounded by the curves y = sin²x, the lines x = 0, y = 0, and x = 1.

4.Let the region bounded by x²+y²=9 be the base of a solid. Find the volume if cross-sections taken perpendicular to the x-axis are isoceles right triangles so that the hypotenuse of the triangle forms the base of the cross-section.

5.The base of a solid is bounded by y = x²and the line y = k. Every cross-section of the solid perpendicular to the y-axis is an isosceles triangle with a height that is three times its base (with the short leg lying in the xy plane). If the volume of the solid is 75, what is the value of k?

Solution

4)it form a cone of height 3 and radius 3

volume=28.26

5)it forms a 1/4 of sphere with r=k

1/4*volume os sphere =75

==k=4.153