Evaluate the Integral $\int _ { 0 } ^ { \sqrt { 2 } } 2 x \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x$

question 51

Multiple Choice

Evaluate the integral. $\int _ { 0 } ^ { \sqrt { 2 } } 2 x \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x$

• A) \(\frac { 2 } { 3 } \left( 11 ^ { \frac { 3 } { 2 } } - 27 \right)\)
• B) \(- \frac { 2 \cdot 11 ^ { \frac { 2 } { 3 } } } { 3 }\)
• C) \(\frac { 2 \cdot 11 ^ { \frac { 3 } { 2 } } } { 3 }\)
• D) \(\frac { 2 } { 3 } \left( 27 - 11 ^ { \frac { 3 } { 2 } } \right)\)
• E) \(\frac { 2 } { 3 } \left( 11 ^ { \frac { 2 } { 3 } } - 27 \right)\)

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Definitions:

Triphosphate Group

A triphosphate group consists of a molecule containing three phosphate groups, and it's most commonly associated with adenosine triphosphate (ATP), which is a primary energy carrier in cells.

Nucleotide

Organic molecules that serve as the monomers of nucleic acids like DNA and RNA, composed of a nitrogenous base, a five-carbon sugar, and one or more phosphate groups.

mRNA

Messenger RNA, a type of RNA that carries instructions from DNA in the nucleus to the ribosome, where proteins are synthesized.

5′ Cap

A modified form of guanine nucleotide added to the 5′ end of eukaryotic mRNA, important for mRNA stability and initiation of translation.