Question

How do you do this question?

Answer 1

3/2

Explanation:

∫ x^(-4/3) dx

Use power rule to evaluate the integral.

-3 x^(-1/3) + C

Evaluate between x=t and x=-8.

[-3 (-8)^(-1/3) + C] − [-3 t^(-1/3) + C]

-3 (-1/2) + C + 3 t^(-1/3) − C

3/2 + 3 t^(-1/3)

Take the limit as t approaches -∞:

lim(t→-∞) [3/2 + 3 t^(-1/3)]

3/2 + 3(0)

3/2