The Volume of the Solid Obtained by Rotating the Plane $y = x ^ { 4 } , y = 1 , \text { and } x = 0$

question 155

Multiple Choice

The volume of the solid obtained by rotating the plane region enclosed by $y = x ^ { 4 } , y = 1 , \text { and } x = 0$ about the x = 1 is

• A) \(\frac { 7 \pi } { 15 }\)
• B) \(\frac { 2 \pi } { 3 }\)
• C) \(\frac { 14 \pi } { 15 }\)
• D) \(\frac { 14 } { 15 }\)
• E) \(\frac { 14 \pi } { 3 }\)
• F) \(\frac { 7 \pi } { 5 }\)
• G) \(\frac { 14 \pi } { 5 }\)
• H) \(\frac { 7 } { 15 }\)

---

Definitions:

Fair Play

A concept embodying fairness, respect, and sportsmanship in both sports and broader contexts.

Double Taxation

The imposition of taxes on the same income, asset, or financial transaction at two different levels of government.

Income Tax

A tax imposed by the government on individuals or entities' income, varying according to income level and filing status.

After-Tax Profits

The net income a company retains after all taxes have been deducted from total revenue.