Find the Length of the Curve $$x = \int _ { y } ^ { 1 } \sqrt { t ^ { 3 } - 1 } d t , 1 \leq y \leq 9$$

question 212

Multiple Choice

Find the length of the curve.
- $$x = \int _ { y } ^ { 1 } \sqrt { t ^ { 3 } - 1 } d t , 1 \leq y \leq 9$$

• A) \(\frac { 484 } { 5 }\)
• B) 20
• C) \(\frac { 481 } { 5 }\)
• D) \(\frac { 52 } { 3 }\)

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Definitions:

Porosity

The measure of void spaces in a material, such as rock or soil, often expressed as a percentage of the total volume.

Natural Cement

Material formed when certain minerals dissolve in water and then precipitate, binding sediment grains together into a solid mass.

Fractures

Breaks or cracks in rock caused by physical stress, often resulting in significant geological structures.

Unsaturated Zone

The layer of ground above the water table where pores are not fully saturated with water.