Decide whether the given integral converges or diverges.

Question

(a)Decide whether the given integral converges or diverges.

+∞

∫9/x^1.5dx

1

(b)If the integral converges, compute its value. (If the integral diverges, enter DNE.)

Answer 1

The integral is equivalent to lim_b→∞ ∫_{(from 1 to b)} [9x^-1.5]dx

= lim_b→∞ [-18/√x]_{(from 1 to b)}

= lim_b→∞ [-18/√b + 18] = 0 + 18 = 18

The integral converges to 18.