Evaluate the Integral Using an Appropriate Trigonometric Substitution $$\int _ { 1 } ^ { 3 } \frac { \sqrt { x ^ { 2 } - 1 } } { x ^ { 4 } } d x$$

question 70

Short Answer

Evaluate the integral using an appropriate trigonometric substitution. $$\int _ { 1 } ^ { 3 } \frac { \sqrt { x ^ { 2 } - 1 } } { x ^ { 4 } } d x$$

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Definitions:

Groundwater Flow

The movement of groundwater through the Earth's subsurface, driven by gravity and differences in pressure.

Subsurface Material

Materials found beneath the Earth's surface, including rocks, minerals, and soil.

Groundwater Velocity

The speed at which groundwater moves through an aquifer, influenced by the permeability of the rock and the hydraulic gradient.

Water Table

The upper surface of the zone of saturation where water pressure and atmospheric pressure are equal, beneath which soil and rock are saturated with water.