Determine Whether the Improper Integral Converges or Diverges, and If $$\int _ { \pi / 2 } ^ { 5 \pi / 6 } \frac { \cos x } { \sqrt { 1 - \sin x } } d x$$

question 26

Short Answer

Determine whether the improper integral converges or diverges, and if it converges, find its value.
$$\int _ { \pi / 2 } ^ { 5 \pi / 6 } \frac { \cos x } { \sqrt { 1 - \sin x } } d x$$

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Definitions:

Marginal Productivity Theory

A principle in economics that suggests the payment to a factor of production (like labor or capital) corresponds to its marginal productivity, which is the additional output generated by one more unit of that factor.

Income Distribution

The way in which total income is shared among individuals or groups within a society.

Perfect Competition

A market structure characterized by a large number of small firms, identical products sold by all firms, freedom of entry and exit, and perfect information about prices and products.

P = MC

The condition where the price of a good equals its marginal cost, representing an equilibrium in perfect competition markets.