Determine whether the improper integral integralinfinity1 11

Determine whether the improper integral integral^infinity_1 1/1.0008 dx converges or diverges, and find the value if it converges. Select the correct choice below and fill in any answer boxes within your choice. A. The value of the integral integral^infinity_1 1/1.0008 dx is B. The integral diverges.

Solution

_{[1 to ]}(1_/x^1.0008) dx

=_{[1 to ]}(x^-1.0008) dx

=_{[1 to ]}((1_/(-1.0008+1))x^-1.0008+1)

=_{[1 to ]}((-1_/0.0008)x^-0.0008)

=(0) -((-1_/0.0008)1^-0.0008)

=(1_/0.0008)

=1250

the value of integral is 1250