Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to

Question

Integral from 1 to 11 of ((11)/(cuberoot(x-1))dx

Answer 1

Since the antiderivative is 11*(3/2)*(x - 1)^(2/3), the discontinuity of the integrand at 1 is no longer a problem. Just evaluate the antiderivative at the given limits.

Answer 2

it is convergent by using fact the region the place the integrand, the expression interior the vital, is going to infinity is -3 this is outdoors one in all those integration. to evaluate it, placed z = x+3, dz = dx and x going from 2 to infinity makes z go from 5 to infinity. The vital reduces to int(5, infinity) z^(-3/2) dz, this is comparable to 0 - 5^(-a million/2)/(-a million/2) . it is two/sqrt(5)