Set Up an Integral for the Length of the Curve $$y = x ^ { 4 } , 0 \leq x \leq 1$$

question 115

Multiple Choice

Set up an integral for the length of the curve.
- $$y = x ^ { 4 } , 0 \leq x \leq 1$$

• A) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 4 x ^ { 3 } } d x\)
• B) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 16 x ^ { 8 } } d x\)
• C) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 4 x ^ { 6 } } d x\)
• D) \(\int _ { 0 } ^ { 1 } \sqrt { 1 + 16 x ^ { 6 } } d x\)

---

Definitions:

Fair Value Method

An accounting approach that measures and reports assets and liabilities at their estimated market value.

Proportionate Interest Goodwill Method

An accounting approach that allocates goodwill based on the proportionate interests of existing owners and new investors in a combination.

Proprietary Concept

A financial accounting principle where the business is considered separate from its owners, focusing on the owner's perspective in accounting records.

Proportional Consolidation Method

An accounting method used when a parent company jointly controls a business entity, consolidating only their proportionate share of the entities' assets, liabilities, and operations.