Evaluate the Integral $\int _ { 0 } ^ { 2 } 3 x \sqrt { 4 x + 4 } \mathrm {~d} x$

question 48

Multiple Choice

Evaluate the integral. $\int _ { 0 } ^ { 2 } 3 x \sqrt { 4 x + 4 } \mathrm {~d} x$

• A) \(0.5 \left( 2 \cdot 12 ^ { 3 } - 0.1 \cdot \left( 12 ^ { 5 } + 2 ^ { 5 } \right) \right)\)
• B) \(0.5 \left( 2 \cdot 12 + 0.1 \cdot \left( 12 ^ { \frac { 2 } { 3 } } + 2 ^ { \frac { 2 } { 3 } } \right) \right)\)
• C) \(0.5 \left( 2 \cdot 12 ^ { \frac { 3 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 5 } { 2 } } - 4 ^ { \frac { 5 } { 2 } } \right) \right)\)
• D) \(0.5 \left( 2 \cdot 12 ^ { \frac { 1 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 3 } { 2 } } - 4 ^ { \frac { 3 } { 2 } } \right) \right)\)
• E) \(0.5 \left( 2 \cdot 12 ^ { \frac { 3 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 1 } { 2 } } - 4 ^ { \frac { 1 } { 2 } } \right) \right)\)

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Definitions:

Extracellular Surface

The exterior part of a cell's structure, interacting with the external environment.

Carrier Proteins

Proteins involved in the movement of ions, small molecules, or macromolecules, such as glucose, across a cell membrane.

Aquaporins

Membrane proteins that serve as channels in the transfer of water, and sometimes small solutes across the cell membrane.

Active Transport

The movement of substances across cell membranes against their concentration gradient, requiring energy expenditure by the cell.