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:

Conscious Movement

Voluntary actions and movements controlled by the brain, reflecting awareness and intent.

Receptor Molecules

Proteins located either on the cell surface or inside of a cell that bind to specific molecules like hormones, neurotransmitters, or drugs, initiating a physiological response.

Muscarinic

Relating to or denoting the type of acetylcholine receptor found in various organs that responds to muscarine.

Adrenergic

Pertaining to the nerve fibers that release adrenaline or neurotransmitters similar to adrenaline, affecting the heart rate, blood pressure, and other physiological responses.