Evaluate the Following Integrals:
(A) $\int _ { 0 } ^ { 1 / 2 } \frac { x } { \sqrt { 1 - x ^ { 2 } } } d x$

question 119

Essay

Evaluate the following integrals:
(a) $\int _ { 0 } ^ { 1 / 2 } \frac { x } { \sqrt { 1 - x ^ { 2 } } } d x$ (b) $\int e ^ { x + e ^ { x } } d x$ (c) $\int \frac { 3 x + 2 } { x - 1 } d x$ (d) $\int \ln \left( 1 + x ^ { 2 } \right) d x$

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Definitions:

Deadweight Loss

A loss of economic efficiency that can occur when the equilibrium for a good or service is not achieved.

Personal Taxes

Taxes levied on individuals' income or wealth by a government.

Progressive Tax

A taxation system in which the tax rate increases as the taxable amount increases, placing a higher burden on those who earn more.

Sales Taxes

Levies imposed by governments on the sale of goods and services, contributing to public revenue.