Consider the Region Bounded by the X-Axis, the Line X $y=x^{2}$

question 63

Multiple Choice

Consider the region bounded by the x-axis, the line x = 1, the line x = 4, and the curve $y=x^{2}$ .Imagine that this region is the base of a solid.Each cross-section of this solid perpendicular to the x-axis is a triangle of height H . The volume of this solid can be found exactly and can be written as $\frac{H B}{6}$ .What is B?

• A) \(63\)
• B) \(15\)
• C) \(3\)
• D) \(64\)

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Definitions:

Adhesion

The tendency of dissimilar particles or surfaces to cling to one another, often causing materials to stick together.

Hydrogen Bonds

Weak bonds between partially positive hydrogen atoms and partially negative elements like oxygen or nitrogen, crucial in biological structures.

pH Scale

A measure of the acidity or basicity of an aqueous solution, ranging from 0 (most acidic) to 14 (most basic) with 7 as neutral.

Hydrogen Ion

A positively charged ion or proton, H+, which is common in acid-base reactions in chemistry and biological systems.