Evaluate the Integral in Terms of Natural Logarithms $$\int _ { 0 } ^ { \sqrt { 2 } / 2 } \frac { 32 \mathrm { dx } } { \sqrt { 1 + 16 \mathrm { x } ^ { 2 } } }$$

question 55

Multiple Choice

Evaluate the integral in terms of natural logarithms.
- $$\int _ { 0 } ^ { \sqrt { 2 } / 2 } \frac { 32 \mathrm { dx } } { \sqrt { 1 + 16 \mathrm { x } ^ { 2 } } }$$

• A) \(\ln 11\)
• B) \(8 \ln ( 2 \sqrt { 2 } + 3 )\)
• C) \(32 \ln ( 2 \sqrt { 2 } + 3 )\)
• D) \(8 \ln ( 2 \sqrt { 2 } + \sqrt { 7 } )\)

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Definitions:

Infinite Recursion

A function that calls itself indefinitely, often resulting in a stack overflow error.

Func1

Typically a placeholder name for a function in programming, implying the first function or a generic function with no specific definition.

Indirectly Recursive

Refers to functions or procedures that call each other in a cycle, rather than one calling itself directly.

Mystery Method

A hypothetical concept referring to an undefined or unnamed method within the context of programming or algorithm analysis.