Set Up an Integral for the Length of the Curve $$y = \sqrt { 1 - x ^ { 8 } } , - \frac { 1 } { 4 } \leq x \leq \frac { 1 } { 4 }$$

question 133

Multiple Choice

Set up an integral for the length of the curve.
- $$y = \sqrt { 1 - x ^ { 8 } } , - \frac { 1 } { 4 } \leq x \leq \frac { 1 } { 4 }$$

• A) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 5 - 4 x ^ { 8 } } { 4 \left( 1 - x ^ { 8 } \right) } } d x\)
• B) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 4 + 64 x ^ { 14 } } { 4 } } d x\)
• C) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 4 - 4 x ^ { 8 } + 8 x ^ { 7 } } { 4 \left( 1 - x ^ { 8 } \right) } } d x\)
• D) \(\int _ { - 1 / 4 } ^ { 1 / 4 } \sqrt { \frac { 4 - 4 x ^ { 8 } + 64 x ^ { 14 } } { 4 \left( 1 - x ^ { 8 } \right) } } d x\)

Comprehend how taxes impact income distribution and inequality.

Understand how the elasticity of demand and supply affects the burden of a tax.

Learn about the major sources of revenue and expenditure for federal, state, and local governments.

Grasp the concept of marginal tax rates and how they apply to additional income.

---

Definitions:

Glycolysis

Glycolysis is a series of enzymatic reactions that break down glucose into pyruvate, producing energy in the form of ATP, and occurs in the cytoplasm of cells.

Lactate Formation

The conversion of pyruvate into lactate by anaerobic glycolysis, often occurring in muscles during intense exercise.

Acetyl-CoA

A molecule that plays a key role in metabolism, particularly in the synthesis and oxidation of fatty acids, and the Krebs cycle.

Citric Acid Cycle

A series of chemical reactions used by all aerobic organisms to generate energy through the oxidation of acetate derived from carbohydrates, fats, and proteins.