Determine whether each integral is convergent or divergent

1- 1/(x-2)^3/2 dx, limits ( infinite to 3)

2- (1/3-4x)dx, limits (0 to -infinite)

3- e^(-5p) dx, limits ( infinite to 2)

4- (x^2/(sqrt(1+x^3)))dx , limits ( infinite to 0)

5- lnx/x dx , limits(infinite to 1)

6- 1/(x^2 +x)dx , limits (infinite to 1)

7- 3/x^5 dx ,limits (1 to 0)

8- dx/(x+2)^1/4 , limits (14 to -2)

9- 1/(x-1)^1/3 , limits (9 to 0)

10- e^x /((e^x) -1), limits (1 to -1)

11- z^2 lnz dz ,limits( 2 to 0)

12- s={(x, y) | x>= 1,0 <= y <=e^-x}

Me. i can't figure out this question. give an explanation too. .

Two triangles can be formed with the given information. use the law of sines to solve the triangles. b = 49°, a = 16, b = 14

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)