Question

Evaluate the following:

Options are:
-12/(5)
0
12/(5)
The integral diverges.

Answer 1

The integral diverges

Explanation:

∫₁³ 2 / (x − 2)^(8/3) dx

∫₁³ 2 (x − 2)^(-8/3) dx

There is a discontinuity in the function at x = 2. Splitting this into two integrals:

∫₁² 2 (x − 2)^(-8/3) dx + ∫₂³ 2 (x − 2)^(-8/3) dx

(-6/5) (x − 2)^(-5/3) |₁² + (-6/5) (x − 2)^(-5/3) |₂³

∞